How to solve 56 h . 7

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 56 h . 7 | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

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

Evaluate

$7\left(\sqrt{2}+\sqrt{3}\right)\approx 22.02385059$

Solution Steps

Rationalize the denominator of $\frac{7}{\sqrt{3}-\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{3}+\sqrt{2}$.

$$\frac{7\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}$$

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

$$\frac{7\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Square $\sqrt{3}$. Square $\sqrt{2}$.

$$\frac{7\left(\sqrt{3}+\sqrt{2}\right)}{3-2}$$

Subtract $2$ from $3$ to get $1$.

$$\frac{7\left(\sqrt{3}+\sqrt{2}\right)}{1}$$

Anything divided by one gives itself.

$$7\left(\sqrt{3}+\sqrt{2}\right)$$

Use the distributive property to multiply $7$ by $\sqrt{3}+\sqrt{2}$.

$$7\sqrt{3}+7\sqrt{2}$$

Show Solution