Solve sqrt{6.67*1.2*4/3*10^14}=

$$\sqrt{ 6.67 \times 1.2 \times \frac{ 4 }{ 3 } \times { 10 }^{ 14 } } =$$

Evaluate

$$400000\sqrt{6670}\approx 32668027.182552669$$

Solution Steps

Multiply 6.67 and 1.2 to get 8.004.

$$\sqrt{8.004\times \frac{4}{3}\times 10^{14}}$$

Convert decimal number 8.004 to fraction \frac{8004}{1000}. Reduce the fraction \frac{8004}{1000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{2001}{250}\times \frac{4}{3}\times 10^{14}}$$

Multiply \frac{2001}{250} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{2001\times 4}{250\times 3}\times 10^{14}}$$

Do the multiplications in the fraction \frac{2001\times 4}{250\times 3}.

$$\sqrt{\frac{8004}{750}\times 10^{14}}$$

Reduce the fraction \frac{8004}{750} to lowest terms by extracting and canceling out 6.

$$\sqrt{\frac{1334}{125}\times 10^{14}}$$

Calculate 10 to the power of 14 and get 100000000000000.

$$\sqrt{\frac{1334}{125}\times 100000000000000}$$

Express \frac{1334}{125}\times 100000000000000 as a single fraction.

$$\sqrt{\frac{1334\times 100000000000000}{125}}$$

Multiply 1334 and 100000000000000 to get 133400000000000000.

$$\sqrt{\frac{133400000000000000}{125}}$$

Divide 133400000000000000 by 125 to get 1067200000000000.

$$\sqrt{1067200000000000}$$

Factor 1067200000000000=400000^{2}\times 6670. Rewrite the square root of the product \sqrt{400000^{2}\times 6670} as the product of square roots \sqrt{400000^{2}}\sqrt{6670}. Take the square root of 400000^{2}.

$$400000\sqrt{6670}$$