# Question on limit with square roots [closed]

I am studying up on my calculus and I have found this limit and I am not sure how to approach this without using L'Hopital's Rule. I am guessing there is an issue with my algebra. Here it is. $$\lim_{x\to 0}\frac{\sqrt{x-x\sqrt{x+x^2}-x^2}}{\sqrt x}$$I am lost on this one! Please help me on this. Thanks.

## closed as off-topic by Ahaan S. Rungta, user7530, user98602, ronno, Ali CaglayanDec 28 '14 at 0:50

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Ahaan S. Rungta, user7530, Community, ronno, Ali Caglayan
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• Show us what you have tried please. – Ahaan S. Rungta Dec 27 '14 at 22:14
• $\lim_{x\to 0} \sqrt{1-\sqrt{x+ x^2}-x}$ – MBYagbasan Dec 27 '14 at 22:17

Note that $$\lim_{x\to 0}\frac{\sqrt{x-x\sqrt{x+x^2}-x^2}}{\sqrt x}=\lim_{x\to 0}\sqrt{\frac{x-x\sqrt{x+x^2}-x^2}{x}}$$Then we have $$=\lim_{x\to 0}\sqrt{1-\sqrt{x+x^2}-x}=1$$