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## Explanation

The sum of a number and its reciprocal is one eighth of 34.

The product of the number and its square root will be figure out in this way.

Let suppose the number is y.

One-eighth of 34

34 x 1/8

The sum of y and 1/y

y + 1/y = 34 x 1/8 ________ (i)

Through equation (i) we can easily find out the value of y (y = 4).

By multiplying the value of “y” with its “square root” we can easily figure out the product as is done in solution.

## To Find

Number = ?

## Solution

Let suppose

Number = y

According to the given condition

y + 1/y = 34 x 1/8

8(y^{2} + 1) = 34y

8y^{2} + 8 = 34y

8y^{2} – 34y + 8 = 0

4y^{2} – 17y + 4 = 0

4y^{2} – 16y – 1y + 4 = 0

4y(y – 4) – 1(y – 4) = 0

(4y – 1)(y – 4) = 0

4y – 1 = 0 & y – 4 = 0

y = 1/4 & y = 4

It means the number is “4”.

The product of the number and its square root

**Required Product = 4 x 2 = 8 answer**

## Conclusion

The sum of a number and its reciprocal is one eighth of 34. The product of the number and its square root is 8.