Trigonometry Examples

$\sqrt{2 \cdot \frac{38}{980}}$

Step 1

Combine $2$ and $\frac{38}{980}$ .

$\sqrt{\frac{2 \cdot 38}{980}}$

Step 2

Reduce the expression $\frac{2 \cdot 38}{980}$ by cancelling the common factors.

Tap for more steps...

Step 2.1

Factor $2$ out of $2 \cdot 38$ .

$\sqrt{\frac{2 (38)}{980}}$

Step 2.2

Factor $2$ out of $980$ .

$\sqrt{\frac{2 \cdot 38}{2 \cdot 490}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{2 \cdot 38}{2 \cdot 490}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{38}{490}}$

Step 3

Cancel the common factor of $38$ and $490$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $38$ .

$\sqrt{\frac{2 (19)}{490}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $490$ .

$\sqrt{\frac{2 \cdot 19}{2 \cdot 245}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{2 \cdot 19}{2 \cdot 245}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{19}{245}}$

Step 4

Rewrite $\sqrt{\frac{19}{245}}$ as $\frac{\sqrt{19}}{\sqrt{245}}$ .

$\frac{\sqrt{19}}{\sqrt{245}}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Rewrite $245$ as $7^{2} \cdot 5$ .

Tap for more steps...

Step 5.1.1

Factor $49$ out of $245$ .

$\frac{\sqrt{19}}{\sqrt{49 (5)}}$

Step 5.1.2

Rewrite $49$ as $7^{2}$ .

$\frac{\sqrt{19}}{\sqrt{7^{2} \cdot 5}}$

Step 5.2

Pull terms out from under the radical.

$\frac{\sqrt{19}}{7 \sqrt{5}}$

Step 6

Multiply $\frac{\sqrt{19}}{7 \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\sqrt{19}}{7 \sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 7

Combine and simplify the denominator.

Tap for more steps...

Step 7.1

Multiply $\frac{\sqrt{19}}{7 \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\sqrt{19} \sqrt{5}}{7 \sqrt{5} \sqrt{5}}$

Step 7.2

Move $\sqrt{5}$ .

$\frac{\sqrt{19} \sqrt{5}}{7 (\sqrt{5} \sqrt{5})}$

Step 7.3

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{\sqrt{19} \sqrt{5}}{7 ({\sqrt{5}}^{1} \sqrt{5})}$

Step 7.4

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{\sqrt{19} \sqrt{5}}{7 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})}$

Step 7.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{19} \sqrt{5}}{7 {\sqrt{5}}^{1 + 1}}$

Step 7.6

Add $1$ and $1$ .

$\frac{\sqrt{19} \sqrt{5}}{7 {\sqrt{5}}^{2}}$

Step 7.7

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Tap for more steps...

Step 7.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{\sqrt{19} \sqrt{5}}{7 {(5^{\frac{1}{2}})}^{2}}$

Step 7.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{19} \sqrt{5}}{7 \cdot 5^{\frac{1}{2} \cdot 2}}$

Step 7.7.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{19} \sqrt{5}}{7 \cdot 5^{\frac{2}{2}}}$

Step 7.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.7.4.1

Cancel the common factor.

$\frac{\sqrt{19} \sqrt{5}}{7 \cdot 5^{\frac{2}{2}}}$

Step 7.7.4.2

Rewrite the expression.

$\frac{\sqrt{19} \sqrt{5}}{7 \cdot 5^{1}}$

Step 7.7.5

Evaluate the exponent.

$\frac{\sqrt{19} \sqrt{5}}{7 \cdot 5}$

Step 8

Simplify the numerator.

Tap for more steps...

Step 8.1

Combine using the product rule for radicals.

$\frac{\sqrt{19 \cdot 5}}{7 \cdot 5}$

Step 8.2

Multiply $19$ by $5$ .

$\frac{\sqrt{95}}{7 \cdot 5}$

Step 9

Multiply $7$ by $5$ .

$\frac{\sqrt{95}}{35}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{95}}{35}$

Decimal Form:

$0.27847983 \dots$