Solve for d d=( square root of 43)^2

$d = {(\sqrt{43})}^{2}$

Step 1

Remove parentheses.

$d = {\sqrt{43}}^{2}$

Step 2

Rewrite ${\sqrt{43}}^{2}$ as $43$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{43}$ as $43^{\frac{1}{2}}$ .

$d = {(43^{\frac{1}{2}})}^{2}$

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

$d = 43^{\frac{1}{2} \cdot 2}$

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

$d = 43^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$d = 43^{\frac{2}{2}}$

Rewrite the expression.

$d = 43^{1}$

Evaluate the exponent.

$d = 43$