Solve 0.7sqrt{100}-1/3sqrt{136}

$$0.7 \sqrt{ 100 } - \frac{ 1 }{ 3 } \sqrt{ 136 }$$

Evaluate

$$-\frac{2\sqrt{34}}{3}+7\approx 3.112698737$$

Solution Steps

Calculate the square root of 100 and get 10.

$$0.7\times 10-\frac{1}{3}\sqrt{136}$$

Multiply 0.7 and 10 to get 7.

$$7-\frac{1}{3}\sqrt{136}$$

Factor 136=2^{2}\times 34. Rewrite the square root of the product \sqrt{2^{2}\times 34} as the product of square roots \sqrt{2^{2}}\sqrt{34}. Take the square root of 2^{2}.

$$7-\frac{1}{3}\times 2\sqrt{34}$$

Express -\frac{1}{3}\times 2 as a single fraction.

$$7+\frac{-2}{3}\sqrt{34}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$7-\frac{2}{3}\sqrt{34}$$

Factor

$$\frac{21 - 2 \sqrt{34}}{3} = 3.1126987367697994$$