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sqrt(75b^(10))

75b10 \sqrt{75 b^{10}}

Full solution

Q. 75b10 \sqrt{75 b^{10}}
  1. Identify Components: Identify the components of the expression.\newlineWe have the square root of 7575 times bb raised to the 1010th power, which is written as 75b10\sqrt{75b^{10}}.
  2. Prime Factorization of 7575: Break down the square root into prime factors for the number 7575.\newline7575 can be factored into 3×253 \times 25, and 2525 is a perfect square (5×55 \times 5).\newlineSo, 75=3×52\sqrt{75} = \sqrt{3 \times 5^2}.
  3. Simplify Perfect Square: Simplify the square root of the perfect square.\newlineSince 525^2 is a perfect square, its square root is 55.\newlineSo, 52=5\sqrt{5^2} = 5.
  4. Apply Square Root to Variable: Apply the square root to the variable with an even exponent.\newlineThe exponent of bb is 1010, which is an even number. The square root of b10b^{10} is bb raised to the power of 102\frac{10}{2}, which is b5b^5.\newlineSo, b10=b5\sqrt{b^{10}} = b^5.
  5. Combine Simplified Components: Combine the simplified components.\newlineWe have 3\sqrt{3} which cannot be simplified further, 55 from the square root of 2525, and b5b^5 from the square root of b10b^{10}.\newlineSo, the simplified form is 5×b5×35 \times b^5 \times \sqrt{3}.

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