How do you solve $\sqrt{\frac{5 y}{6}} - 10 = 4$ $sqrt((5y)/6)-10=4$ and check your solution?

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How do you solve $\sqrt{\frac{5 y}{6}} - 10 = 4$ $sqrt((5y)/6)-10=4$ and check your solution?

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Answer 1 · 2017-05-31T00:59:18

See a solution process below:

Explanation:

First, add $10$ $color(red)(10)$ to each side of the equation to isolate the radical while keeping the equation balanced:

$\sqrt{\frac{5 y}{6}} - 10 + 10 = 4 + 10$ $sqrt((5y)/6) - 10 + color(red)(10) = 4 + color(red)(10)$

$\sqrt{\frac{5 y}{6}} - 0 = 14$ $sqrt((5y)/6) - 0 = 14$

$\sqrt{\frac{5 y}{6}} = 14$ $sqrt((5y)/6) = 14$

Next, square each side of the equation to eliminate the radical while keeping the equation balanced:

${(\sqrt{\frac{5 y}{6}})}^{2} = 14^{2}$ $(sqrt((5y)/6))^2 = 14^2$

$\frac{5 y}{6} = 196$ $(5y)/6 = 196$

Now, multiply each side of the equation by $\frac{6}{5}$ $color(red)(6)/color(blue)(5)$ to solve for $y$ $y$ while keeping the equation balanced:

$\frac{6}{5} \times \frac{5 y}{6} = \frac{6}{5} \times 196$ $color(red)(6)/color(blue)(5) xx (5y)/6 = color(red)(6)/color(blue)(5) xx 196$

$cancel(color(red)(6))/cancel(color(blue)(5)) xx (color(blue)(cancel(color(black)(5)))y)/color(red)(cancel(color(black)(6))) = 1176/5$

$y = 1176/5$

To check the solution we need to substitute $color(red)(1176/5)$ for $color(red)(y)$ , calculate each side of the equation and ensure the two results are equal:

$sqrt((5color(red)(y))/6) - 10 = 4$ becomes:

$sqrt((5 xx color(red)(1176/5))/6) - 10 = 4$

$sqrt((color(red)(cancel(color(black)(5))) xx color(red)(1176/color(black)(cancel(color(red)(5)))))/6) - 10 = 4$

$sqrt(1176/6) - 10 = 4$

$+-sqrt(196) - 10 = 4$

$+-14 - 10 = 4$

$4 = 4$ or $-24 = 4$

The $-14$ result of the square root is extraneous.

Therefore, $4 = 4$ and the solution is shown to be correct.

Answer 2 · 2017-05-31T01:04:14

$y = 235.2$

Explanation:

$sqrt((5y)/6) - 10 = 4$

$sqrt((5y)/6) = 4 + 10$

$sqrt((5y)/6) = 14$

$(5y)/6 = 14^2$

$(5y)/6 = 196$

$5y = 196 xx 6$

$5y = 1176$

$y = 1176 ÷ 5$

$color(blue)(y = 235.2$

We can now substitute $y$ for $235.2$ to prove our answer.

$sqrt((5y)/6) - 10 = 4$

$sqrt((5 xx 235.2)/6) - 10 = 4$

$sqrt(1176/6) - 10 = 4$

$sqrt(196) - 10 = 4$

$14 - 10 = 4$

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How do you solve $\sqrt{\frac{5 y}{6}} - 10 = 4$ $sqrt((5y)/6)-10=4$ and check your solution?

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