Solve (5sqrt{48}-6sqrt{4}+4sqrt{15})divsqrt{3}

$$( 5 \sqrt { 48 } - 6 \sqrt { 4 } + 4 \sqrt { 15 } ) \div \sqrt { 3 }$$

Evaluate

$$\frac{12\sqrt{5}}{3}+20-4\sqrt{3}\approx 22.01606868$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{5\times 4\sqrt{3}-6\sqrt{4}+4\sqrt{15}}{\sqrt{3}}$$

Multiply 5 and 4 to get 20.

$$\frac{20\sqrt{3}-6\sqrt{4}+4\sqrt{15}}{\sqrt{3}}$$

Calculate the square root of 4 and get 2.

$$\frac{20\sqrt{3}-6\times 2+4\sqrt{15}}{\sqrt{3}}$$

Multiply -6 and 2 to get -12.

$$\frac{20\sqrt{3}-12+4\sqrt{15}}{\sqrt{3}}$$

Rationalize the denominator of \frac{20\sqrt{3}-12+4\sqrt{15}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(20\sqrt{3}-12+4\sqrt{15}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(20\sqrt{3}-12+4\sqrt{15}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 20\sqrt{3}-12+4\sqrt{15} by \sqrt{3}.

$$\frac{20\left(\sqrt{3}\right)^{2}-12\sqrt{3}+4\sqrt{15}\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{20\times 3-12\sqrt{3}+4\sqrt{15}\sqrt{3}}{3}$$

Multiply 20 and 3 to get 60.

$$\frac{60-12\sqrt{3}+4\sqrt{15}\sqrt{3}}{3}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$\frac{60-12\sqrt{3}+4\sqrt{3}\sqrt{5}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{60-12\sqrt{3}+4\times 3\sqrt{5}}{3}$$

Multiply 4 and 3 to get 12.

$$\frac{60-12\sqrt{3}+12\sqrt{5}}{3}$$