Trigonometry Examples

$\sqrt{{(7)}^{2} - {(\sqrt{7})}^{2}} \cdot 7$

Step 1

Raise $7$ to the power of $2$ .

$\sqrt{49 - {(\sqrt{7})}^{2}} \cdot 7$

Step 2

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\sqrt{49 - {(7^{\frac{1}{2}})}^{2}} \cdot 7$

Step 2.2

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

$\sqrt{49 - 7^{\frac{1}{2} \cdot 2}} \cdot 7$

Step 2.3

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

$\sqrt{49 - 7^{\frac{2}{2}}} \cdot 7$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$\sqrt{49 - 7^{\frac{2}{2}}} \cdot 7$

Step 2.4.2

Rewrite the expression.

$\sqrt{49 - 7^{1}} \cdot 7$

Step 2.5

Evaluate the exponent.

$\sqrt{49 - 1 \cdot 7} \cdot 7$

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 1$ by $7$ .

$\sqrt{49 - 7} \cdot 7$

Step 3.2

Subtract $7$ from $49$ .

$\sqrt{42} \cdot 7$

Step 3.3

Move $7$ to the left of $\sqrt{42}$ .

$7 \sqrt{42}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{42}$

Decimal Form:

$45.36518488 \dots$