Solve 25*sqrt{251*12sqrt{sqrt{sqrt{sqrt{/}}}}}

$$25 \times \sqrt{ 251 \times 12 \sqrt{ \sqrt{ \sqrt{ \sqrt{ \frac{ }{ } } } } } }$$

Evaluate

$$50\sqrt{753}\approx 1372.042273401$$

Solution Steps

Divide 1 by 1 to get 1.

$$25\sqrt{251\times 12\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}$$

Multiply 251 and 12 to get 3012.

$$25\sqrt{3012\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}$$

Calculate the square root of 1 and get 1.

$$25\sqrt{3012\sqrt{\sqrt{\sqrt{1}}}}$$

Calculate the square root of 1 and get 1.

$$25\sqrt{3012\sqrt{\sqrt{1}}}$$

Calculate the square root of 1 and get 1.

$$25\sqrt{3012\sqrt{1}}$$

Calculate the square root of 1 and get 1.

$$25\sqrt{3012\times 1}$$

Multiply 3012 and 1 to get 3012.

$$25\sqrt{3012}$$

Factor 3012=2^{2}\times 753. Rewrite the square root of the product \sqrt{2^{2}\times 753} as the product of square roots \sqrt{2^{2}}\sqrt{753}. Take the square root of 2^{2}.

$$25\times 2\sqrt{753}$$

Multiply 25 and 2 to get 50.

$$50\sqrt{753}$$