Solve sqrt((7-1)^(2)-(3-1)^(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

$$\sqrt{ { \left(7-1 \right) }^{ 2 } - { \left(3-1 \right) }^{ 2 } }$$

Evaluate

$4\sqrt{2}\approx 5.656854249$

Solution Steps

Subtract $1$ from $7$ to get $6$.

$$\sqrt{6^{2}-\left(3-1\right)^{2}}$$

Calculate $6$ to the power of $2$ and get $36$.

$$\sqrt{36-\left(3-1\right)^{2}}$$

Subtract $1$ from $3$ to get $2$.

$$\sqrt{36-2^{2}}$$

Calculate $2$ to the power of $2$ and get $4$.

$$\sqrt{36-4}$$

Subtract $4$ from $36$ to get $32$.

$$\sqrt{32}$$

Factor $32=4^{2}\times 2$. Rewrite the square root of the product $\sqrt{4^{2}\times 2}$ as the product of square roots $\sqrt{4^{2}}\sqrt{2}$. Take the square root of $4^{2}$.

$$4\sqrt{2}$$