Solve 0.3*98*2/sqrt{3+0.3}

$$\frac{ 0.3 \times 98 \times 2 }{ \sqrt{ 3 } +0.3 }$$

Evaluate

$$\frac{1960\sqrt{3}-588}{97}\approx 28.936284359$$

Solution Steps

Multiply 0.3 and 98 to get 29.4.

$$\frac{29.4\times 2}{\sqrt{3}+0.3}$$

Multiply 29.4 and 2 to get 58.8.

$$\frac{58.8}{\sqrt{3}+0.3}$$

Rationalize the denominator of \frac{58.8}{\sqrt{3}+0.3} by multiplying numerator and denominator by \sqrt{3}-0.3.

$$\frac{58.8\left(\sqrt{3}-0.3\right)}{\left(\sqrt{3}+0.3\right)\left(\sqrt{3}-0.3\right)}$$

Consider \left(\sqrt{3}+0.3\right)\left(\sqrt{3}-0.3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{58.8\left(\sqrt{3}-0.3\right)}{\left(\sqrt{3}\right)^{2}-0.3^{2}}$$

Square \sqrt{3}. Square 0.3.

$$\frac{58.8\left(\sqrt{3}-0.3\right)}{3-0.09}$$

Subtract 0.09 from 3 to get 2.91.

$$\frac{58.8\left(\sqrt{3}-0.3\right)}{2.91}$$

Divide 58.8\left(\sqrt{3}-0.3\right) by 2.91 to get \frac{1960}{97}\left(\sqrt{3}-0.3\right).

$$\frac{1960}{97}\left(\sqrt{3}-0.3\right)$$

Use the distributive property to multiply \frac{1960}{97} by \sqrt{3}-0.3.

$$\frac{1960}{97}\sqrt{3}-\frac{588}{97}$$