Question

1. simplify the expression: $3\sqrt{50} + 3\sqrt{32}$

a $\sqrt{82}$
b $6\sqrt{2}$
c $15\sqrt{2}$
d $27\sqrt{2}$

Explanation:

Step1: Simplify each square root

Simplify \( \sqrt{50} \) and \( \sqrt{32} \). We know that \( \sqrt{50} = \sqrt{25\times2} = \sqrt{25}\times\sqrt{2} = 5\sqrt{2} \) and \( \sqrt{32} = \sqrt{16\times2} = \sqrt{16}\times\sqrt{2} = 4\sqrt{2} \).

Step2: Substitute back into the expression

Substitute these simplified forms into the original expression \( 3\sqrt{50} + 3\sqrt{32} \). So we get \( 3\times5\sqrt{2} + 3\times4\sqrt{2} \).

Step3: Perform the multiplications

Calculate \( 3\times5\sqrt{2} = 15\sqrt{2} \) and \( 3\times4\sqrt{2} = 12\sqrt{2} \).

Step4: Combine like terms

Add the two terms together: \( 15\sqrt{2} + 12\sqrt{2} = (15 + 12)\sqrt{2} = 27\sqrt{2} \).

Answer:

D. \( 27\sqrt{2} \)