Question

$4m {}^{2}= 3$
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Answer 1

Answer:

$m=-\frac{\sqrt3}{2}\ and\ m=\frac{\sqrt3}{2}$

Step-by-step explanation:

Given:

The equation given to solve is:

$4m^2=3$

First, we divide both sides by 4. This gives,

$\frac{4m^2}{4}=\frac{3}{4}\\\\m^2=\frac{3}{4}$

Now, we take square root on both sides. This gives,

$\sqrt{m^2}=\pm\sqrt{\frac{3}{4}}$

We know that from the definition of square root function that:

$\sqrt{x^2}=x$

$\sqrt{\frac{x}{y}}=\frac{\sqrt{x}}{\sqrt{y}}$

Therefore,

$\sqrt{m^2}=m$

$\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{\sqrt{4}}=\frac{\sqrt3}{2}$

$m=\pm\frac{\sqrt3}{2}$

Hence, two values of 'm' are possible. They are:

$m=-\frac{\sqrt3}{2}\ and\ m=\frac{\sqrt3}{2}$