Solve sqrt{17(17-12)*(17-12)*(17-12)*(17-10)}

$$\sqrt{ 17(17-12) \times (17-12) \times (17-12) \times (17-10) }$$

Evaluate

$$5\sqrt{595}\approx 121.963109177$$

Solution Steps

Multiply 17-12 and 17-12 to get \left(17-12\right)^{2}.

$$\sqrt{17\left(17-12\right)^{2}\left(17-12\right)\left(17-10\right)}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\sqrt{17\left(17-12\right)^{3}\left(17-10\right)}$$

Subtract 12 from 17 to get 5.

$$\sqrt{17\times 5^{3}\left(17-10\right)}$$

Calculate 5 to the power of 3 and get 125.

$$\sqrt{17\times 125\left(17-10\right)}$$

Multiply 17 and 125 to get 2125.

$$\sqrt{2125\left(17-10\right)}$$

Subtract 10 from 17 to get 7.

$$\sqrt{2125\times 7}$$

Multiply 2125 and 7 to get 14875.

$$\sqrt{14875}$$

Factor 14875=5^{2}\times 595. Rewrite the square root of the product \sqrt{5^{2}\times 595} as the product of square roots \sqrt{5^{2}}\sqrt{595}. Take the square root of 5^{2}.

$$5\sqrt{595}$$