Solve \sqrt { 5 } ( 7 \sqrt { 10 } + 2 \sqrt { 3 } )

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$\sqrt { 5 } ( 7 \sqrt { 10 } + 2 \sqrt { 3 } )$$

$\sqrt{2}\left(\sqrt{30}+35\right)\approx 57.243441375$

Use the distributive property to multiply $\sqrt{5}$ by $7\sqrt{10}+2\sqrt{3}$.

$$7\sqrt{5}\sqrt{10}+2\sqrt{5}\sqrt{3}$$

Factor $10=5\times 2$. Rewrite the square root of the product $\sqrt{5\times 2}$ as the product of square roots $\sqrt{5}\sqrt{2}$.

$$7\sqrt{5}\sqrt{5}\sqrt{2}+2\sqrt{5}\sqrt{3}$$

Multiply $\sqrt{5}$ and $\sqrt{5}$ to get $5$.

$$7\times 5\sqrt{2}+2\sqrt{5}\sqrt{3}$$

Multiply $7$ and $5$ to get $35$.

$$35\sqrt{2}+2\sqrt{5}\sqrt{3}$$

To multiply $\sqrt{5}$ and $\sqrt{3}$, multiply the numbers under the square root.

$$35\sqrt{2}+2\sqrt{15}$$