Solve 3sqrt{48}+2sqrt{32}+sqrt{98}-(4sqrt{27}+sqrt{450})

$$3 \sqrt { 48 } + 2 \sqrt { 32 } + \sqrt { 98 } - ( 4 \sqrt { 27 } + \sqrt { 450 } )$$

Evaluate

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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}.

$$3\times 4\sqrt{3}+2\sqrt{32}+\sqrt{98}-\left(4\sqrt{27}+\sqrt{450}\right)$$

Multiply 3 and 4 to get 12.

$$12\sqrt{3}+2\sqrt{32}+\sqrt{98}-\left(4\sqrt{27}+\sqrt{450}\right)$$

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}.

$$12\sqrt{3}+2\times 4\sqrt{2}+\sqrt{98}-\left(4\sqrt{27}+\sqrt{450}\right)$$

Multiply 2 and 4 to get 8.

$$12\sqrt{3}+8\sqrt{2}+\sqrt{98}-\left(4\sqrt{27}+\sqrt{450}\right)$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$12\sqrt{3}+8\sqrt{2}+7\sqrt{2}-\left(4\sqrt{27}+\sqrt{450}\right)$$

Combine 8\sqrt{2} and 7\sqrt{2} to get 15\sqrt{2}.

$$12\sqrt{3}+15\sqrt{2}-\left(4\sqrt{27}+\sqrt{450}\right)$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$12\sqrt{3}+15\sqrt{2}-\left(4\times 3\sqrt{3}+\sqrt{450}\right)$$

Multiply 4 and 3 to get 12.

$$12\sqrt{3}+15\sqrt{2}-\left(12\sqrt{3}+\sqrt{450}\right)$$

Factor 450=15^{2}\times 2. Rewrite the square root of the product \sqrt{15^{2}\times 2} as the product of square roots \sqrt{15^{2}}\sqrt{2}. Take the square root of 15^{2}.

$$12\sqrt{3}+15\sqrt{2}-\left(12\sqrt{3}+15\sqrt{2}\right)$$

Combine 12\sqrt{3}+15\sqrt{2} and -\left(12\sqrt{3}+15\sqrt{2}\right) to get 0.

$$0$$

Factor

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