Solve 4sqrt{a}=sqrt{4a+27}

$$4 \sqrt { a } = \sqrt { 4 a + 27 }$$

Solve for a

$$a = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

Solution Steps

Square both sides of the equation.

$$\left(4\sqrt{a}\right)^{2}=\left(\sqrt{4a+27}\right)^{2}$$

Expand \left(4\sqrt{a}\right)^{2}.

$$4^{2}\left(\sqrt{a}\right)^{2}=\left(\sqrt{4a+27}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{a}\right)^{2}=\left(\sqrt{4a+27}\right)^{2}$$

Calculate \sqrt{a} to the power of 2 and get a.

$$16a=\left(\sqrt{4a+27}\right)^{2}$$

Calculate \sqrt{4a+27} to the power of 2 and get 4a+27.

$$16a=4a+27$$

Subtract 4a from both sides.

$$16a-4a=27$$

Combine 16a and -4a to get 12a.

$$12a=27$$

Divide both sides by 12.

$$a=\frac{27}{12}$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$a=\frac{9}{4}$$

Substitute \frac{9}{4} for a in the equation 4\sqrt{a}=\sqrt{4a+27}.

$$4\sqrt{\frac{9}{4}}=\sqrt{4\times \frac{9}{4}+27}$$

Simplify. The value a=\frac{9}{4} satisfies the equation.

$$6=6$$

Equation 4\sqrt{a}=\sqrt{4a+27} has a unique solution.

$$a=\frac{9}{4}$$