Solve -7sqrt{142}+9sqrt{72}-15sqrt{32}

$$-7 \sqrt{ 142 } +9 \sqrt{ 72 } -15 \sqrt{ 32 }$$

Evaluate

$$-6\sqrt{2}-7\sqrt{142}\approx -91.899908389$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$-7\sqrt{142}+9\times 6\sqrt{2}-15\sqrt{32}$$

Multiply 9 and 6 to get 54.

$$-7\sqrt{142}+54\sqrt{2}-15\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$-7\sqrt{142}+54\sqrt{2}-15\times 4\sqrt{2}$$

Multiply -15 and 4 to get -60.

$$-7\sqrt{142}+54\sqrt{2}-60\sqrt{2}$$

Combine 54\sqrt{2} and -60\sqrt{2} to get -6\sqrt{2}.

$$-7\sqrt{142}-6\sqrt{2}$$