Solve for t square root of 2t-7 = square root of t+2

$\sqrt{2 t - 7} = \sqrt{t + 2}$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{2 t - 7}}^{2} = {\sqrt{t + 2}}^{2}$

Simplify each side of the equation.

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

${({(2 t - 7)}^{\frac{1}{2}})}^{2} = {\sqrt{t + 2}}^{2}$

Simplify the left side.

Simplify ${({(2 t - 7)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 t - 7)}^{\frac{1}{2}})}^{2}$ .

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

${(2 t - 7)}^{\frac{1}{2} \cdot 2} = {\sqrt{t + 2}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 t - 7)}^{\frac{1}{2} \cdot 2} = {\sqrt{t + 2}}^{2}$

Rewrite the expression.

${(2 t - 7)}^{1} = {\sqrt{t + 2}}^{2}$

Simplify.

$2 t - 7 = {\sqrt{t + 2}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{t + 2}}^{2}$ as $t + 2$ .

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

$2 t - 7 = {({(t + 2)}^{\frac{1}{2}})}^{2}$

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

$2 t - 7 = {(t + 2)}^{\frac{1}{2} \cdot 2}$

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

$2 t - 7 = {(t + 2)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 t - 7 = {(t + 2)}^{\frac{2}{2}}$

Rewrite the expression.

$2 t - 7 = {(t + 2)}^{1}$

Simplify.

$2 t - 7 = t + 2$

Solve for $t$ .

Move all terms containing $t$ to the left side of the equation.

Subtract $t$ from both sides of the equation.

$2 t - 7 - t = 2$

Subtract $t$ from $2 t$ .

$t - 7 = 2$

Move all terms not containing $t$ to the right side of the equation.

Add $7$ to both sides of the equation.

$t = 2 + 7$

Add $2$ and $7$ .

$t = 9$