QuestionCalculate the value of $5+\sqrt{108}$ .

Studdy Solution

STEP 1

Question: What is the structure of the given expression $5+\sqrt{108}$ ?
A) A quadratic expression B) A summation of a constant and a square root C) A product of a constant and a square root D) A division of a constant by a square root
Answer: B) A summation of a constant and a square root

STEP 2

Question: What is the prime factorization of 108?
A) $2^3 \times 3^2$ B) $2^2 \times 3^2$ C) $2^2 \times 3^3$ D) $2^3 \times 3^3$
Answer: C) $2^2 \times 3^3$

STEP 3

Question: How should we simplify the square root in the expression $\sqrt{108}$ ?
A) $\sqrt{2^2} \times \sqrt{3^3}$ B) $2 \times 3 \times \sqrt{2}$ C) $2 \times 3 \times \sqrt{3}$ D) $2 \times 3 \times \sqrt{6}$
Answer: C) $2 \times 3 \times \sqrt{3}$

STEP 4

Question: Simplify the multiplication in the expression $2 \times 3 \times \sqrt{3}$ .
A) $6\sqrt{3}$ B) $5\sqrt{3}$ C) $9\sqrt{3}$ D) $12\sqrt{3}$
Answer: A) $6\sqrt{3}$

STEP 5

Question: What is the simplified form of the expression $5+\sqrt{108}$ ?
A) $5 + 6\sqrt{3}$ B) $11\sqrt{3}$ C) $5 + 3\sqrt{6}$ D) $11\sqrt{6}$
Answer: A) $5 + 6\sqrt{3}$

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