We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# help

0
167
2

What is the least possible positive integer-value of N such that $$\sqrt{18 \cdot n \cdot 34}$$ is an integer?

Jul 13, 2019

### 2+0 Answers

#1
+8829
+5

$$\phantom{=\quad}\sqrt{18\cdot n\cdot34}\\~\\ {=\quad}\sqrt{3\cdot3\cdot2\cdot n\cdot2\cdot17}\\~\\ {=\quad}\sqrt{3\cdot3\cdot2\cdot 2\cdot17\cdot n}\\~\\ {=\quad}\sqrt{3\cdot3}\cdot\sqrt{2\cdot 2}\cdot\sqrt{17\cdot n}\\~\\ {=\quad}3\cdot2\cdot\sqrt{17\cdot n}\\~\\ {=\quad}6\sqrt{17n}$$

There must be a pair of  17's  in the prime factorization of the number under the sqrt.

So  17  must be a factor of  n  , and the least possible positive integer value of  n  is  17

$$\phantom{=\quad}6\sqrt{17\cdot17}\\~\\ {=\quad}6\cdot17\\~\\ {=\quad}102$$_

Jul 13, 2019
#2
+2484
+2

In these problems, simplify the radical so its easier to understand.

CalculatorUser  Jul 13, 2019