Solve (sqrt(3) - sqrt(5)) ^ 2 | 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

$$(\sqrt{3}-\sqrt{5})^{2}$$

Evaluate

$8-2\sqrt{15}\approx 0.254033308$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(\sqrt{3}-\sqrt{5}\right)^{2}$.

$$\left(\sqrt{3}\right)^{2}-2\sqrt{3}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

The square of $\sqrt{3}$ is $3$.

$$3-2\sqrt{3}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

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

$$3-2\sqrt{15}+\left(\sqrt{5}\right)^{2}$$

The square of $\sqrt{5}$ is $5$.

$$3-2\sqrt{15}+5$$

Add $3$ and $5$ to get $8$.

$$8-2\sqrt{15}$$

Expand

$8-2\sqrt{15}$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(\sqrt{3}-\sqrt{5}\right)^{2}$.

$$\left(\sqrt{3}\right)^{2}-2\sqrt{3}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

The square of $\sqrt{3}$ is $3$.

$$3-2\sqrt{3}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

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

$$3-2\sqrt{15}+\left(\sqrt{5}\right)^{2}$$

The square of $\sqrt{5}$ is $5$.

$$3-2\sqrt{15}+5$$

Add $3$ and $5$ to get $8$.

$$8-2\sqrt{15}$$