Simplify. Assume x is greater than or equal to zero. sqrt 84x ______

Find Prime Factors: sqrt(84x) First, let's find the prime factors of the number 84. Prime factorization of a number is the product of its prime factors. sqrt(84x) = sqrt(2 * 2 * 3 * 7 * x)Group Identical Factors: sqrt(2 * 2 * 3 * 7 * x) Now, group the identical factors and use the exponents for them. sqrt(2 * 2 * 3 * 7 * x) = sqrt(2^2 * 3 * 7 * x)Apply Product Property: sqrt(2^2 * 3 * 7 * x) Apply the product property of radicals, which allows us to take the square root of each factor separately. sqrt(2^2 * 3 * 7 * x) = sqrt(2^2) * sqrt(3) * sqrt(7) * sqrt(x)Simplify Square Roots: sqrt(2^2) * sqrt(3) * sqrt(7) * sqrt(x) Since the square root and the square cancel each other out, we can simplify sqrt(2^2) to 2. sqrt(2^2) * sqrt(3) * sqrt(7) * sqrt(x) = 2 * sqrt(3) * sqrt(7) * sqrt(x)Combine Remaining Square Roots: 2 * sqrt(3) * sqrt(7) * sqrt(x) Since there are no more identical factors to combine, and we cannot simplify the square roots of 3, 7, or x any further, we can combine the remaining square roots under one radical. 2 * sqrt(3) * sqrt(7) * sqrt(x) = 2 * sqrt(3 * 7 * x)Multiply Numbers Under Square Root: 2 * sqrt(3 * 7 * x) Now, multiply the numbers under the square root. 2 * sqrt(3 * 7 * x) = 2 * sqrt(21x)Final Simplification: Final Simplification The final simplified form of sqrt(84x) is 2 * sqrt(21x).

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Simplify. Assume $x$ is greater than or equal to zero. $\newline$ $\sqrt{84x}$

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Q. Simplify. Assume

x

is greater than or equal to zero.

\newline

\sqrt{84x}

Find Prime Factors: $\sqrt{84x}$ $\newline$ First, let's find the prime factors of the number $84$ . $\newline$ Prime factorization of a number is the product of its prime factors. $\newline$ $\sqrt{84x} = \sqrt{2 \times 2 \times 3 \times 7 \times x}$
Group Identical Factors: $\sqrt{2 \times 2 \times 3 \times 7 \times x}$ $\newline$ Now, group the identical factors and use the exponents for them. $\newline$ $\sqrt{2 \times 2 \times 3 \times 7 \times x} = \sqrt{2^2 \times 3 \times 7 \times x}$
Apply Product Property: $\sqrt{2^2 \times 3 \times 7 \times x}$ Apply the product property of radicals, which allows us to take the square root of each factor separately. $\sqrt{2^2 \times 3 \times 7 \times x} = \sqrt{2^2} \times \sqrt{3} \times \sqrt{7} \times \sqrt{x}$
Simplify Square Roots: $\sqrt{2^2} \times \sqrt{3} \times \sqrt{7} \times \sqrt{x}$ $\newline$ Since the square root and the square cancel each other out, we can simplify $\sqrt{2^2}$ to $2$ . $\newline$ $\sqrt{2^2} \times \sqrt{3} \times \sqrt{7} \times \sqrt{x} = 2 \times \sqrt{3} \times \sqrt{7} \times \sqrt{x}$
Combine Remaining Square Roots: $2 \times \sqrt{3} \times \sqrt{7} \times \sqrt{x}$ $\newline$ Since there are no more identical factors to combine, and we cannot simplify the square roots of $3$ , $7$ , or $x$ any further, we can combine the remaining square roots under one radical. $\newline$ $2 \times \sqrt{3} \times \sqrt{7} \times \sqrt{x} = 2 \times \sqrt{3 \times 7 \times x}$
Multiply Numbers Under Square Root: $2 \times \sqrt{3 \times 7 \times x}$ $\newline$ Now, multiply the numbers under the square root. $\newline$ $2 \times \sqrt{3 \times 7 \times x} = 2 \times \sqrt{21x}$
Final Simplification: Final Simplification $\newline$ The final simplified form of $\sqrt{84x}$ is $2 \times \sqrt{21x}$ .