Math / Numbers & Operations

QuestionExpress the radical in simplified form. 4) $\sqrt{72}$

Studdy Solution

STEP 1

1. We need to simplify the radical expression $\sqrt{72}$ .
2. Simplifying a radical involves factoring out perfect squares from under the square root.

STEP 2

1. Factor the number under the square root.
2. Identify and extract perfect square factors.
3. Simplify the radical expression.

STEP 3

Factor $72$ into its prime factors.
$72 = 2 \times 36 = 2 \times 6 \times 6 = 2 \times 2 \times 3 \times 2 \times 3$

STEP 4

Identify the perfect square factors from the prime factorization.
From the factorization $72 = 2^3 \times 3^2$ , the perfect square is $36 = 6^2$ .

STEP 5

Extract the perfect square from under the square root.
$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$
The simplified form of the radical is:
$\boxed{6\sqrt{2}}$

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QuestionExpress the radical in simplified form. 4) $\sqrt{72}$

Studdy Solution

STEP 1

1. We need to simplify the radical expression $\sqrt{72}$ .
2. Simplifying a radical involves factoring out perfect squares from under the square root.

STEP 2

1. Factor the number under the square root.
2. Identify and extract perfect square factors.
3. Simplify the radical expression.

STEP 3

Factor $72$ into its prime factors.
$72 = 2 \times 36 = 2 \times 6 \times 6 = 2 \times 2 \times 3 \times 2 \times 3$

STEP 4

Identify the perfect square factors from the prime factorization.
From the factorization $72 = 2^3 \times 3^2$ , the perfect square is $36 = 6^2$ .

STEP 5

Extract the perfect square from under the square root.
$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$
The simplified form of the radical is:
$\boxed{6\sqrt{2}}$

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QuestionExpress the radical in simplified form. 4) 72\sqrt{72}72​

Studdy Solution

STEP 1

1. We need to simplify the radical expression 72\sqrt{72}72​.2. Simplifying a radical involves factoring out perfect squares from under the square root.

STEP 2

1. Factor the number under the square root.2. Identify and extract perfect square factors.3. Simplify the radical expression.

STEP 3

Factor 727272 into its prime factors.72=2×36=2×6×6=2×2×3×2×3 72 = 2 \times 36 = 2 \times 6 \times 6 = 2 \times 2 \times 3 \times 2 \times 3 72=2×36=2×6×6=2×2×3×2×3

STEP 4

Identify the perfect square factors from the prime factorization.From the factorization 72=23×3272 = 2^3 \times 3^272=23×32, the perfect square is 36=6236 = 6^236=62.

STEP 5

Extract the perfect square from under the square root.72=36×2=36×2=62\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}72​=36×2​=36​×2​=62​ The simplified form of the radical is:62\boxed{6\sqrt{2}}62​​

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QuestionExpress the radical in simplified form. 4) $\sqrt{72}$

1. We need to simplify the radical expression $\sqrt{72}$ .
2. Simplifying a radical involves factoring out perfect squares from under the square root.

1. Factor the number under the square root.
2. Identify and extract perfect square factors.
3. Simplify the radical expression.

Factor $72$ into its prime factors.
$72 = 2 \times 36 = 2 \times 6 \times 6 = 2 \times 2 \times 3 \times 2 \times 3$

Identify the perfect square factors from the prime factorization.
From the factorization $72 = 2^3 \times 3^2$ , the perfect square is $36 = 6^2$ .

Extract the perfect square from under the square root.
$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$
The simplified form of the radical is:
$\boxed{6\sqrt{2}}$