Solve 10=sqrt{5(5-a)(5-3)(5-2}

$$10 = \sqrt { 5 ( 5 - a ) ( 5 - 3 ) ( 5 - 2 }$$

Solve for a

$$a = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Radical Equations

Subtract 3 from 5 to get 2.

$$10=\sqrt{5\left(5-a\right)\times 2\left(5-2\right)}$$

Multiply 5 and 2 to get 10.

$$10=\sqrt{10\left(5-a\right)\left(5-2\right)}$$

Subtract 2 from 5 to get 3.

$$10=\sqrt{10\left(5-a\right)\times 3}$$

Multiply 10 and 3 to get 30.

$$10=\sqrt{30\left(5-a\right)}$$

Use the distributive property to multiply 30 by 5-a.

$$10=\sqrt{150-30a}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{150-30a}=10$$

Square both sides of the equation.

$$-30a+150=100$$

Subtract 150 from both sides of the equation.

$$-30a+150-150=100-150$$

Subtracting 150 from itself leaves 0.

$$-30a=100-150$$

Subtract 150 from 100.

$$-30a=-50$$

Divide both sides by -30.

$$\frac{-30a}{-30}=-\frac{50}{-30}$$

Dividing by -30 undoes the multiplication by -30.

$$a=-\frac{50}{-30}$$

Reduce the fraction \frac{-50}{-30} to lowest terms by extracting and canceling out 10.

$$a=\frac{5}{3}$$