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(b+4sqrtb)^(2)=5

$(b+4 \sqrt{b})^{2}=5$

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Simplify radical expressions involving fractions

Full solution

Q.

(b+4 \sqrt{b})^{2}=5

Expand Expression: Expand the expression using the formula $(a+b)^2 = a^2 + 2ab + b^2$ . $(b + 4\sqrt{b})^2 = b^2 + 2(b)(4\sqrt{b}) + (4\sqrt{b})^2$
Calculate Terms: Calculate each term separately. $\newline$ $b^2 = b \times b$ $\newline$ $2(b)(4\sqrt{b}) = 8b \times \sqrt{b}$ $\newline$ $(4\sqrt{b})^2 = (4\sqrt{b}) \times (4\sqrt{b})$
Simplify Terms: Simplify the terms. $\newline$ $b^2 = b^2$ $\newline$ $8b \cdot \sqrt{b} = 8b^{\frac{3}{2}}$ $\newline$ $(4\sqrt{b}) \cdot (4\sqrt{b}) = 16b$
Combine Final Expression: Combine the terms to get the final expression. $\newline$ $(b+4\sqrt{b})^2 = b^2 + 8b^{\frac{3}{2}} + 16b$
Set Equal to $5$ : Set the expression equal to $5$ as given in the problem. $b^2 + 8b^{\frac{3}{2}} + 16b = 5$

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