Solve sqrt{4^2+(15-5*5)^2}

$$\sqrt { 4 ^ { 2 } + ( 15 - 5 \cdot 5 ) ^ { 2 } }$$

Evaluate

$$2\sqrt{29}\approx 10.770329614$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16+\left(15-5\times 5\right)^{2}}$$

Multiply 5 and 5 to get 25.

$$\sqrt{16+\left(15-25\right)^{2}}$$

Subtract 25 from 15 to get -10.

$$\sqrt{16+\left(-10\right)^{2}}$$

Calculate -10 to the power of 2 and get 100.

$$\sqrt{16+100}$$

Add 16 and 100 to get 116.

$$\sqrt{116}$$

Factor 116=2^{2}\times 29. Rewrite the square root of the product \sqrt{2^{2}\times 29} as the product of square roots \sqrt{2^{2}}\sqrt{29}. Take the square root of 2^{2}.

$$2\sqrt{29}$$