Solve (12sqrt{2})^2=12^2+5^2

$$( 12 \sqrt { 2 } ) ^ { 2 } = 12 ^ { 2 } + 5 ^ { 2 }$$

Verify

Solution Steps

Expand \left(12\sqrt{2}\right)^{2}.

$$12^{2}\left(\sqrt{2}\right)^{2}=12^{2}+5^{2}$$

Calculate 12 to the power of 2 and get 144.

$$144\left(\sqrt{2}\right)^{2}=12^{2}+5^{2}$$

The square of \sqrt{2} is 2.

$$144\times 2=12^{2}+5^{2}$$

Multiply 144 and 2 to get 288.

$$288=12^{2}+5^{2}$$

Calculate 12 to the power of 2 and get 144.

$$288=144+5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$288=144+25$$

Add 144 and 25 to get 169.

$$288=169$$

Compare 288 and 169.

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