Simplify. Assume w is greater than or equal to zero. sqrt 350w^7 ______

Factorize 350 and w^7: sqrt(350w^7) First, let's find the prime factors of the number 350 and express w^7 in terms of w^2. Prime factorization of 350 is 2 * 5 * 5 * 7. sqrt(350w^7) = sqrt(2 * 5^2 * 7 * w^7)Group identical factors: sqrt(2 * 5^2 * 7 * w^7) Now, group the identical factors and express w^7 as (w^2)^3 * w to separate the perfect squares. sqrt(2 * 5^2 * 7 * w^7) = sqrt(2 * 5^2 * 7 * (w^2)^3 * w)Apply product property of radicals: sqrt(2 * 5^2 * 7 * (w^2)^3 * w) Apply the product property of radicals to separate the perfect squares from the non-perfect squares. sqrt(2 * 5^2 * 7 * (w^2)^3 * w) = sqrt(5^2) * sqrt((w^2)^3) * sqrt(2 * 7 * w)Simplify perfect squares: sqrt(5^2) * sqrt((w^2)^3) * sqrt(2 * 7 * w) Simplify the square roots of the perfect squares. sqrt(5^2) * sqrt((w^2)^3) * sqrt(2 * 7 * w) = 5 * w^3 * sqrt(14w)Final simplified form: 5 * w^3 * sqrt(14w) This is the simplified form of the original expression.

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Simplify. Assume $w$ is greater than or equal to zero. $\newline$ $\sqrt{350w^7}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify. Assume

w

is greater than or equal to zero.

\newline

\sqrt{350w^7}

Factorize $350$ and $w^7$ : $\sqrt{350w^7}$ $\newline$ First, let's find the prime factors of the number $350$ and express $w^7$ in terms of $w^2$ . $\newline$ Prime factorization of $350$ is $2 \times 5 \times 5 \times 7$ . $\newline$ $\sqrt{350w^7} = \sqrt{2 \times 5^2 \times 7 \times w^7}$
Group identical factors: $\sqrt{2 \times 5^2 \times 7 \times w^7}$ $\newline$ Now, group the identical factors and express $w^7$ as $(w^2)^3 \times w$ to separate the perfect squares. $\newline$ $\sqrt{2 \times 5^2 \times 7 \times w^7} = \sqrt{2 \times 5^2 \times 7 \times (w^2)^3 \times w}$
Apply product property of radicals: $\sqrt{2 \times 5^2 \times 7 \times (w^2)^3 \times w}$ Apply the product property of radicals to separate the perfect squares from the non-perfect squares. $\sqrt{2 \times 5^2 \times 7 \times (w^2)^3 \times w} = \sqrt{5^2} \times \sqrt{(w^2)^3} \times \sqrt{2 \times 7 \times w}$
Simplify perfect squares: $\sqrt{5^2} \times \sqrt{(w^2)^3} \times \sqrt{2 \times 7 \times w}$ $\newline$ Simplify the square roots of the perfect squares. $\newline$ $\sqrt{5^2} \times \sqrt{(w^2)^3} \times \sqrt{2 \times 7 \times w} = 5 \times w^3 \times \sqrt{14w}$
Final simplified form: $5 \cdot w^3 \cdot \sqrt{14w}$ $\newline$ This is the simplified form of the original expression.