8.6 Solve Radical Equations

Before you get started, take this readiness quiz.

Simplify: $\left(y - 3\right)^{2} .$
If you missed this problem, review the reference.

Solve: $2 x - 5 = 0 .$
If you missed this problem, review the reference.

Solve $n^{2} - 6 n + 8 = 0 .$
If you missed this problem, review the reference.

Solve: $\sqrt{3 m + 2} - 5 = 0 .$

Solve: $\sqrt{10 z + 1} - 2 = 0 .$

Solve: $\sqrt{2 r - 3} + 5 = 0 .$

Solve: $\sqrt{7 s - 3} + 2 = 0 .$

Solve: $\sqrt{x - 2} + 2 = x .$

Solve: $\sqrt{y - 5} + 5 = y .$

Solve: $\sqrt[3]{4 x - 3} + 8 = 5$

Solve: $\sqrt[3]{6 x - 10} + 1 = −3$

Solve: $\left(9 x + 9\right)^{\frac{1}{4}} - 2 = 1 .$

Solve: $\left(4 x - 8\right)^{\frac{1}{4}} + 5 = 7 .$

Solve: $\sqrt{m + 9} - m + 3 = 0 .$

Solve: $\sqrt{n + 1} - n + 1 = 0 .$

Solve: $2 \sqrt{4 a + 4} - 16 = 16 .$

Solve: $3 \sqrt{2 b + 3} - 25 = 50 .$

Solve: $\sqrt[3]{4 x - 3} = \sqrt[3]{3 x + 2} .$

Solve: $\sqrt[3]{5 x - 4} = \sqrt[3]{2 x + 5} .$

Solve: $\sqrt[3]{7 x + 1} = \sqrt[3]{2 x - 5} .$

Solve: $3 - \sqrt{x} = \sqrt{x - 3} .$

Solve: $\sqrt{x} + 2 = \sqrt{x + 16} .$

Solve: $\sqrt{x - 1} + 2 = \sqrt{2 x + 6}$

Solve: $\sqrt{x} + 2 = \sqrt{3 x + 4}$

A helicopter dropped a rescue package from a height of 1,296 feet. Use the formula $t = \frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the ground.

A window washer dropped a squeegee from a platform 196 feet above the sidewalk Use the formula $t = \frac{\sqrt{h}}{4}$ to find how many seconds it took for the squeegee to reach the sidewalk.

An accident investigator measured the skid marks of the car. The length of the skid marks was 76 feet. Use the formula $s = \sqrt{24 d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

The skid marks of a vehicle involved in an accident were 122 feet long. Use the formula $s = \sqrt{24 d}$ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

Solve.

$\sqrt{5 x - 6} = 8$

Solve.

$\sqrt{5 x + 1} = −3$

Solve.

$\sqrt[3]{2 x} = −2$

Solve.

$\sqrt{2 m - 3} - 5 = 0$

Solve.

$\sqrt{6 v - 2} - 10 = 0$

Solve.

$\sqrt{4 m + 2} + 2 = 6$

Solve.

$\sqrt{2 u - 3} + 2 = 0$

Solve.

$\sqrt{u - 3} + 3 = u$

Solve.

$\sqrt{r - 1} = r - 1$

Solve.

$\sqrt[3]{6 x + 4} = 4$

Solve.

$\sqrt[3]{4 x + 5} - 2 = −5$

Solve.

$\left(6 x + 1\right)^{\frac{1}{2}} - 3 = 4$

Solve.

$\left(8 x + 5\right)^{\frac{1}{3}} + 2 = −1$

Solve.

$\left(12 x - 3\right)^{\frac{1}{4}} - 5 = −2$

Solve.

$\sqrt{x + 1} - x + 1 = 0$

Solve.

$\sqrt{z + 100} - z = −10$

Solve.

$3 \sqrt{2 x - 3} - 20 = 7$

Solve.

$2 \sqrt{8 r + 1} - 8 = 2$

Solve.

$\sqrt{3 u + 7} = \sqrt{5 u + 1}$

Solve.

$\sqrt{8 + 2 r} = \sqrt{3 r + 10}$

Solve.

$\sqrt[3]{5 x - 1} = \sqrt[3]{x + 3}$

Solve.

$\sqrt[3]{2 x^{2} + 9 x - 18} = \sqrt[3]{x^{2} + 3 x - 2}$

Solve.

$\sqrt{a} + 2 = \sqrt{a + 4}$

Solve.

$\sqrt{u} + 1 = \sqrt{u + 4}$

Solve.

$\sqrt{a + 5} - \sqrt{a} = 1$

Solve.

$\sqrt{2 x + 1} = 1 + \sqrt{x}$

Solve.

$\sqrt{2 x - 1} - \sqrt{x - 1} = 1$

Solve.

$\sqrt{x + 7} - \sqrt{x - 5} = 2$

Solve. Round approximations to one decimal place.

Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of 75 square feet. Use the formula $s = \sqrt{A}$ to find the length of each side of his garden. Round your answer to the nearest tenth of a foot.

Solve. Round approximations to one decimal place.

Gravity A hang glider dropped his cell phone from a height of 350 feet. Use the formula $t = \frac{\sqrt{h}}{4}$ to find how many seconds it took for the cell phone to reach the ground.

Solve. Round approximations to one decimal place.

Accident investigation The skid marks for a car involved in an accident measured 216 feet. Use the formula $s = \sqrt{24 d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

Explain why an equation of the form $\sqrt{x} + 1 = 0$ has no solution.