Solve sqrt{32(32-6)(32-11)}(32div15)

$$\sqrt { 32 ( 32 - 6 ) ( 32 - 11 ) } ( 32 \div 15 )$$

Evaluate

$$\frac{256\sqrt{273}}{15}\approx 281.987612021$$

Solution Steps

Subtract 6 from 32 to get 26.

$$\sqrt{32\times 26\left(32-11\right)}\times \frac{32}{15}$$

Multiply 32 and 26 to get 832.

$$\sqrt{832\left(32-11\right)}\times \frac{32}{15}$$

Subtract 11 from 32 to get 21.

$$\sqrt{832\times 21}\times \frac{32}{15}$$

Multiply 832 and 21 to get 17472.

$$\sqrt{17472}\times \frac{32}{15}$$

Factor 17472=8^{2}\times 273. Rewrite the square root of the product \sqrt{8^{2}\times 273} as the product of square roots \sqrt{8^{2}}\sqrt{273}. Take the square root of 8^{2}.

$$8\sqrt{273}\times \frac{32}{15}$$

Express 8\times \frac{32}{15} as a single fraction.

$$\frac{8\times 32}{15}\sqrt{273}$$

Multiply 8 and 32 to get 256.

$$\frac{256}{15}\sqrt{273}$$