Trigonometry Examples

$\sqrt{\frac{2 (572 - 421 - 144)}{18}}$

Step 1

Simplify by subtracting numbers.

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Step 1.1

Subtract $421$ from $572$ .

$\sqrt{\frac{2 (151 - 144)}{18}}$

Step 1.2

Subtract $144$ from $151$ .

$\sqrt{\frac{2 \cdot 7}{18}}$

Step 2

Reduce the expression $\frac{2 \cdot 7}{18}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $2 \cdot 7$ .

$\sqrt{\frac{2 (7)}{18}}$

Step 2.2

Factor $2$ out of $18$ .

$\sqrt{\frac{2 \cdot 7}{2 \cdot 9}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{2 \cdot 7}{2 \cdot 9}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{7}{9}}$

Step 3

Rewrite $\sqrt{\frac{7}{9}}$ as $\frac{\sqrt{7}}{\sqrt{9}}$ .

$\frac{\sqrt{7}}{\sqrt{9}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{7}}{\sqrt{3^{2}}}$

Step 4.2

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

$\frac{\sqrt{7}}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{7}}{3}$

Decimal Form:

$0.88191710 \dots$