Solve 3sqrt{48}+sqrt{108}-2sqrt{147}=

$$3 \sqrt { 48 } + \sqrt { 108 } - 2 \sqrt { 147 } =$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$3\times 4\sqrt{3}+\sqrt{108}-2\sqrt{147}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{3}+\sqrt{108}-2\sqrt{147}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$12\sqrt{3}+6\sqrt{3}-2\sqrt{147}$$

Combine 12\sqrt{3} and 6\sqrt{3} to get 18\sqrt{3}.

$$18\sqrt{3}-2\sqrt{147}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$18\sqrt{3}-2\times 7\sqrt{3}$$

Multiply -2 and 7 to get -14.

$$18\sqrt{3}-14\sqrt{3}$$

Combine 18\sqrt{3} and -14\sqrt{3} to get 4\sqrt{3}.

$$4\sqrt{3}$$