Solve 4sqrt{12}a=b

$$4 \sqrt { 12 } a = b$$

Solve for a

$$a=\frac{\sqrt{3}b}{24}$$

Steps for Solving Linear Equation

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$4\times 2\sqrt{3}a=b$$

Multiply 4 and 2 to get 8.

$$8\sqrt{3}a=b$$

Divide both sides by 8\sqrt{3}.

$$\frac{8\sqrt{3}a}{8\sqrt{3}}=\frac{b}{8\sqrt{3}}$$

Dividing by 8\sqrt{3} undoes the multiplication by 8\sqrt{3}.

$$a=\frac{b}{8\sqrt{3}}$$

Divide b by 8\sqrt{3}.

$$a=\frac{\sqrt{3}b}{24}$$

Solve for b

$$b=8\sqrt{3}a$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$4\times 2\sqrt{3}a=b$$

Multiply 4 and 2 to get 8.

$$8\sqrt{3}a=b$$

Swap sides so that all variable terms are on the left hand side.

$$b=8\sqrt{3}a$$