Solve (sqrt(48) + sqrt(17))(sqrt(53) - sqrt(16)) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(\sqrt{48}+\sqrt{17})(\sqrt{53}-\sqrt{16})$$

Evaluate

$\sqrt{901}+4\sqrt{159}-4\sqrt{17}-16\sqrt{3}\approx 36.249507468$

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 $4^{2}$.

$$\left(4\sqrt{3}+\sqrt{17}\right)\left(\sqrt{53}-\sqrt{16}\right)$$

Calculate the square root of $16$ and get $4$.

$$\left(4\sqrt{3}+\sqrt{17}\right)\left(\sqrt{53}-4\right)$$

Apply the distributive property by multiplying each term of $4\sqrt{3}+\sqrt{17}$ by each term of $\sqrt{53}-4$.

$$4\sqrt{3}\sqrt{53}-16\sqrt{3}+\sqrt{17}\sqrt{53}-4\sqrt{17}$$

To multiply $\sqrt{3}$ and $\sqrt{53}$, multiply the numbers under the square root.

$$4\sqrt{159}-16\sqrt{3}+\sqrt{17}\sqrt{53}-4\sqrt{17}$$

To multiply $\sqrt{17}$ and $\sqrt{53}$, multiply the numbers under the square root.

$$4\sqrt{159}-16\sqrt{3}+\sqrt{901}-4\sqrt{17}$$