Finite Math Examples

\sqrt{\frac{{(1 - 3)}^{2} + {(1 - 3)}^{2} + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{{(1 - 3)}^{2} + {(1 - 3)}^{2} + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 1

Subtract

3

$3$ from

1

$1$ .

\sqrt{\frac{{(- 2)}^{2} + {(1 - 3)}^{2} + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{{(- 2)}^{2} + {(1 - 3)}^{2} + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 2

Raise

- 2

$- 2$ to the power of

2

$2$ .

\sqrt{\frac{4 + {(1 - 3)}^{2} + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + {(1 - 3)}^{2} + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 3

Subtract

3

$3$ from

1

$1$ .

\sqrt{\frac{4 + {(- 2)}^{2} + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + {(- 2)}^{2} + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 4

Raise

- 2

$- 2$ to the power of

2

$2$ .

\sqrt{\frac{4 + 4 + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + {(2 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 5

Subtract

3

$3$ from

2

$2$ .

\sqrt{\frac{4 + 4 + {(- 1)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + {(- 1)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 6

Raise

- 1

$- 1$ to the power of

2

$2$ .

\sqrt{\frac{4 + 4 + 1 + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 7

Subtract

3

$3$ from

3

$3$ .

\sqrt{\frac{4 + 4 + 1 + 0^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0^{2} + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 8

Raising

0

$0$ to any positive power yields

0

$0$ .

\sqrt{\frac{4 + 4 + 1 + 0 + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + {(3 - 3)}^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 9

Subtract

3

$3$ from

3

$3$ .

\sqrt{\frac{4 + 4 + 1 + 0 + 0^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0^{2} + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 10

Raising

0

$0$ to any positive power yields

0

$0$ .

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + {(3 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 11

Subtract

3

$3$ from

3

$3$ .

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 12

Raising

0

$0$ to any positive power yields

0

$0$ .

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 13

Subtract

3

$3$ from

4

$4$ .

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1^{2} + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 14

One to any power is one.

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + {(4 - 3)}^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 15

Subtract

3

$3$ from

4

$4$ .

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1^{2} + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 16

One to any power is one.

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + {(4 - 3)}^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 17

Subtract

3

$3$ from

4

$4$ .

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 1^{2} + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 1^{2} + {(5 - 3)}^{2}}{10 - 1}}$

Step 18

One to any power is one.

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 1 + {(5 - 3)}^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 1 + {(5 - 3)}^{2}}{10 - 1}}$

Step 19

Subtract

3

$3$ from

5

$5$ .

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 1 + 2^{2}}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 1 + 2^{2}}{10 - 1}}$

Step 20

Raise

2

$2$ to the power of

2

$2$ .

\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 1 + 4}{10 - 1}}

$\sqrt{\frac{4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 1 + 4}{10 - 1}}$

Step 21

Add

4

$4$ and

4

$4$ .

\sqrt{\frac{8 + 1 + 0 + 0 + 0 + 1 + 1 + 1 + 4}{10 - 1}}

$\sqrt{\frac{8 + 1 + 0 + 0 + 0 + 1 + 1 + 1 + 4}{10 - 1}}$

Step 22

Add

8

$8$ and

1

$1$ .

\sqrt{\frac{9 + 0 + 0 + 0 + 1 + 1 + 1 + 4}{10 - 1}}

$\sqrt{\frac{9 + 0 + 0 + 0 + 1 + 1 + 1 + 4}{10 - 1}}$

Step 23

Add

9

$9$ and

0

$0$ .

\sqrt{\frac{9 + 0 + 0 + 1 + 1 + 1 + 4}{10 - 1}}

$\sqrt{\frac{9 + 0 + 0 + 1 + 1 + 1 + 4}{10 - 1}}$

Step 24

Add

9

$9$ and

0

$0$ .

\sqrt{\frac{9 + 0 + 1 + 1 + 1 + 4}{10 - 1}}

$\sqrt{\frac{9 + 0 + 1 + 1 + 1 + 4}{10 - 1}}$

Step 25

Add

9

$9$ and

0

$0$ .

\sqrt{\frac{9 + 1 + 1 + 1 + 4}{10 - 1}}

$\sqrt{\frac{9 + 1 + 1 + 1 + 4}{10 - 1}}$

Step 26

Add

9

$9$ and

1

$1$ .

\sqrt{\frac{10 + 1 + 1 + 4}{10 - 1}}

$\sqrt{\frac{10 + 1 + 1 + 4}{10 - 1}}$

Step 27

Add

10

$10$ and

1

$1$ .

\sqrt{\frac{11 + 1 + 4}{10 - 1}}

$\sqrt{\frac{11 + 1 + 4}{10 - 1}}$

Step 28

Add

11

$11$ and

1

$1$ .

\sqrt{\frac{12 + 4}{10 - 1}}

$\sqrt{\frac{12 + 4}{10 - 1}}$

Step 29

Add

12

$12$ and

4

$4$ .

\sqrt{\frac{16}{10 - 1}}

$\sqrt{\frac{16}{10 - 1}}$

Step 30

Subtract

1

$1$ from

10

$10$ .

\sqrt{\frac{16}{9}}

$\sqrt{\frac{16}{9}}$

Step 31

Rewrite

\sqrt{\frac{16}{9}}

$\sqrt{\frac{16}{9}}$ as

\frac{\sqrt{16}}{\sqrt{9}}

$\frac{\sqrt{16}}{\sqrt{9}}$ .

\frac{\sqrt{16}}{\sqrt{9}}

$\frac{\sqrt{16}}{\sqrt{9}}$

Step 32

Simplify the numerator.

Tap for more steps...

Step 32.1

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

\frac{\sqrt{4^{2}}}{\sqrt{9}}

$\frac{\sqrt{4^{2}}}{\sqrt{9}}$

Step 32.2

Pull terms out from under the radical, assuming positive real numbers.

\frac{4}{\sqrt{9}}

$\frac{4}{\sqrt{9}}$

\frac{4}{\sqrt{9}}

$\frac{4}{\sqrt{9}}$

Step 33

Simplify the denominator.

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Step 33.1

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

\frac{4}{\sqrt{3^{2}}}

$\frac{4}{\sqrt{3^{2}}}$

Step 33.2

Pull terms out from under the radical, assuming positive real numbers.

\frac{4}{3}

$\frac{4}{3}$

\frac{4}{3}

$\frac{4}{3}$

Step 34

The result can be shown in multiple forms.

Exact Form:

\frac{4}{3}

$\frac{4}{3}$

Decimal Form:

1. ¯ 3

$1.\overline{3}$

Mixed Number Form:

1 \frac{1}{3}

$1 \frac{1}{3}$