CCSS.HSN.RN.A.2.Q.NQ.RE.1 - Simplify the radical expression √3(√3 + √12)

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

STEP 1: Recall what is a radical

STEP 2: Recall what is a radical expression

STEP 3: Recall what are prime factors of a number

STEP 4: Recall what is the distributive property in the radical expression

STEP 5: Simplify

Using the distributive property multiply \sqrt{3} with \sqrt{3} and multiply \sqrt{3} with \sqrt{12} to get

\sqrt{3 \times 3} + \sqrt{3 \times 12}

\sqrt{3 \times 3 } + \sqrt{ 3 \times 2\times 2 \times 3}

\sqrt{3 ^{2}}+\sqrt{3^{2} \times 2^{2}} (using the property of exponents - when bases are equal the powers can be added)

3 + \sqrt{(3 \times 2 \times 2 \times 3)}

3 + ( 3 \times 2)

= 3 + 6 = 9