Solve 3sqrt{5a}*sqrt{5a}

$$3 \sqrt { 5 a } \times \sqrt { 5 a }$$

Evaluate

$$15a$$

Solution Steps

Multiply \sqrt{5a} and \sqrt{5a} to get \left(\sqrt{5a}\right)^{2}.

$$3\left(\sqrt{5a}\right)^{2}$$

Calculate \sqrt{5a} to the power of 2 and get 5a.

$$3\times 5a$$

Multiply 3 and 5 to get 15.

$$15a$$

Differentiate w.r.t. a

$$15$$

Steps Using Definition of a Derivative

Multiply \sqrt{5a} and \sqrt{5a} to get \left(\sqrt{5a}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3\left(\sqrt{5a}\right)^{2})$$

Calculate \sqrt{5a} to the power of 2 and get 5a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3\times 5a)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}a}(15a)$$

The derivative of ax^{n} is nax^{n-1}.

$$15a^{1-1}$$

Subtract 1 from 1.

$$15a^{0}$$

For any term t except 0, t^{0}=1.

$$15\times 1$$

For any term t, t\times 1=t and 1t=t.

$$15$$