Solve 70/3sqrt{455-6}

$$\frac{ 70 }{ 3 \sqrt{ 455 } -6 }$$

Evaluate

$$\frac{70\left(\sqrt{455}+2\right)}{1353}\approx 1.20705915$$

Solution Steps

Rationalize the denominator of \frac{70}{3\sqrt{455}-6} by multiplying numerator and denominator by 3\sqrt{455}+6.

$$\frac{70\left(3\sqrt{455}+6\right)}{\left(3\sqrt{455}-6\right)\left(3\sqrt{455}+6\right)}$$

Consider \left(3\sqrt{455}-6\right)\left(3\sqrt{455}+6\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{70\left(3\sqrt{455}+6\right)}{\left(3\sqrt{455}\right)^{2}-6^{2}}$$

Expand \left(3\sqrt{455}\right)^{2}.

$$\frac{70\left(3\sqrt{455}+6\right)}{3^{2}\left(\sqrt{455}\right)^{2}-6^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{70\left(3\sqrt{455}+6\right)}{9\left(\sqrt{455}\right)^{2}-6^{2}}$$

The square of \sqrt{455} is 455.

$$\frac{70\left(3\sqrt{455}+6\right)}{9\times 455-6^{2}}$$

Multiply 9 and 455 to get 4095.

$$\frac{70\left(3\sqrt{455}+6\right)}{4095-6^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{70\left(3\sqrt{455}+6\right)}{4095-36}$$

Subtract 36 from 4095 to get 4059.

$$\frac{70\left(3\sqrt{455}+6\right)}{4059}$$

Use the distributive property to multiply 70 by 3\sqrt{455}+6.

$$\frac{210\sqrt{455}+420}{4059}$$