Solve 5sqrt{16}5sqrt{2}

$$5 \sqrt{ 16 } 5 \sqrt{ 2 }$$

Evaluate

$$100\sqrt{2}\approx 141.421356237$$

Solution Steps

Factor 16=2\times 8. Rewrite the square root of the product \sqrt{2\times 8} as the product of square roots \sqrt{2}\sqrt{8}.

$$5\times 5\sqrt{2}\sqrt{8}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$5\times 5\times 2\sqrt{8}$$

Multiply 5 and 5 to get 25.

$$25\times 2\sqrt{8}$$

Multiply 25 and 2 to get 50.

$$50\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$50\times 2\sqrt{2}$$

Multiply 50 and 2 to get 100.

$$100\sqrt{2}$$