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Simplify 75b10 \sqrt{75b^{10}} assuming b b is greater than or equal to 0 0 .

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Full solution

Q. Simplify 75b10 \sqrt{75b^{10}} assuming b b is greater than or equal to 0 0 .
  1. Prime factorize: 75b10 \sqrt{75b^{10}} Prime factorize the radicand. 75b10=3⋅52⋅b10 \sqrt{75b^{10}} = \sqrt{3 \cdot 5^2 \cdot b^{10}}
  2. Group identical factors: 3⋅52⋅b10 \sqrt{3 \cdot 5^2 \cdot b^{10}} Group the identical factors. 3⋅52⋅b10=3⋅52⋅(b5)2 \sqrt{3 \cdot 5^2 \cdot b^{10}} = \sqrt{3 \cdot 5^2 \cdot (b^5)^2}
  3. Use product property: 3⋅52⋅(b5)2 \sqrt{3 \cdot 5^2 \cdot (b^5)^2}
    Use the product property of radicals.
    3⋅52⋅(b5)2=3⋅52⋅(b5)2 \sqrt{3 \cdot 5^2 \cdot (b^5)^2} = \sqrt{3} \cdot \sqrt{5^2} \cdot \sqrt{(b^5)^2}
  4. Simplify square roots: 3×52×(b5)2 \sqrt{3} \times \sqrt{5^2} \times \sqrt{(b^5)^2} Simplify the square roots. 3×5×b5 \sqrt{3} \times 5 \times b^5
  5. Combine terms: 3 \sqrt{3} * 5 5 * b5 b^5 Combine the terms. 5b53 5b^5\sqrt{3}

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