Solve sqrt{4*160*10^3/3.14*170.10^6}

$$\sqrt { \frac { 4 \times 160 \times 10 ^ { 3 } } { 3.14 \times 170.10 ^ { 6 } } }$$

Evaluate

$$\frac{4000000\sqrt{314}}{772702990857}\approx 0.00009173$$

Solution Steps

Multiply 4 and 160 to get 640.

$$\sqrt{\frac{640\times 10^{3}}{3.14\times 170.1^{6}}}$$

Calculate 10 to the power of 3 and get 1000.

$$\sqrt{\frac{640\times 1000}{3.14\times 170.1^{6}}}$$

Multiply 640 and 1000 to get 640000.

$$\sqrt{\frac{640000}{3.14\times 170.1^{6}}}$$

Calculate 170.1 to the power of 6 and get 24222885799803.360201.

$$\sqrt{\frac{640000}{3.14\times 24222885799803.360201}}$$

Multiply 3.14 and 24222885799803.360201 to get 76059861411382.55103114.

$$\sqrt{\frac{640000}{76059861411382.55103114}}$$

Expand \frac{640000}{76059861411382.55103114} by multiplying both numerator and the denominator by 100000000.

$$\sqrt{\frac{64000000000000}{7605986141138255103114}}$$

Reduce the fraction \frac{64000000000000}{7605986141138255103114} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{32000000000000}{3802993070569127551557}}$$

Rewrite the square root of the division \sqrt{\frac{32000000000000}{3802993070569127551557}} as the division of square roots \frac{\sqrt{32000000000000}}{\sqrt{3802993070569127551557}}.

$$\frac{\sqrt{32000000000000}}{\sqrt{3802993070569127551557}}$$

Factor 32000000000000=4000000^{2}\times 2. Rewrite the square root of the product \sqrt{4000000^{2}\times 2} as the product of square roots \sqrt{4000000^{2}}\sqrt{2}. Take the square root of 4000000^{2}.

$$\frac{4000000\sqrt{2}}{\sqrt{3802993070569127551557}}$$

Factor 3802993070569127551557=4921675101^{2}\times 157. Rewrite the square root of the product \sqrt{4921675101^{2}\times 157} as the product of square roots \sqrt{4921675101^{2}}\sqrt{157}. Take the square root of 4921675101^{2}.

$$\frac{4000000\sqrt{2}}{4921675101\sqrt{157}}$$

Rationalize the denominator of \frac{4000000\sqrt{2}}{4921675101\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{4000000\sqrt{2}\sqrt{157}}{4921675101\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{4000000\sqrt{2}\sqrt{157}}{4921675101\times 157}$$

To multiply \sqrt{2} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{4000000\sqrt{314}}{4921675101\times 157}$$

Multiply 4921675101 and 157 to get 772702990857.

$$\frac{4000000\sqrt{314}}{772702990857}$$