Solve 1+8divsqrt{8}

$$1 + 8 \div \sqrt { 8 }$$

Evaluate

$$2\sqrt{2}+1\approx 3.828427125$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$1+\frac{8}{2\sqrt{2}}$$

Rationalize the denominator of \frac{8}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$1+\frac{8\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$1+\frac{8\sqrt{2}}{2\times 2}$$

Cancel out 2\times 2 in both numerator and denominator.

$$1+2\sqrt{2}$$