Solve (sqrt{3}+sqrt{12})^2=27

$$( \sqrt { 3 } + \sqrt { 12 } ) ^ { 2 } = 27$$

Verify

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\left(\sqrt{3}+2\sqrt{3}\right)^{2}=27$$

Combine \sqrt{3} and 2\sqrt{3} to get 3\sqrt{3}.

$$\left(3\sqrt{3}\right)^{2}=27$$

Expand \left(3\sqrt{3}\right)^{2}.

$$3^{2}\left(\sqrt{3}\right)^{2}=27$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{3}\right)^{2}=27$$

The square of \sqrt{3} is 3.

$$9\times 3=27$$

Multiply 9 and 3 to get 27.

$$27=27$$

Compare 27 and 27.

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