Evaluate the radical. − 1 4 -\sqrt{\frac14} − 4 1 <path d="M983 90l0 -0c4,-6.7,10,-10,18,-10 H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5zM1001 80h400000v40h-400000z">

Hey, everyone. So let's get started here. We're gonna evaluate this radical. Now this is kind of weird because we haven't seen radicals with fractions yet, but, basically, this just means exactly like what they do with whole numbers. I just need to do I just need to find some number that multiplies by itself to give me 1 fourth. Now one of the things you might remember from fractions is that the only way I can get a fraction is by multiplying 2 other fractions. So how does this work? I basically I'm just gonna do like, I have to do a number that multiplied by itself gives me 1 fourth. Alright? And I know that this thing has to be a fraction. So can we think of some numbers? Let's try one over 8 and eights. Well, one over eights times one over eights doesn't give me the 4 because you have to multiply the denominators and that gets me to 64. So that's not gonna work. What about 3 and 3? Well, 3 and 3 will give me 9 over here. That's not gonna work. What if I do 2 in the denominators? 2 times 2 will get me to 4 in the denominator. So, basically, what ends up happening is that 1 half is the fraction that you have to multiply by itself to get you to 1 fourth. So what that means here, this symbol means, remember the radical means the positive root, but if I have a negative sign out here, it's looking for the negative roots because, again, negative one half times negative one half also gets me to 1 fourth. So it's asking for one of the roots, either one half or negative one half. And remember, because of this negative sign out here, you have to look at the negative roots. So this is really just negative one half, and that's your final answer. Alright? So that's what that means. Let me know if you have any questions. Thanks for watching.

Evaluate the radical. − 1 4 -\sqrt{\frac14} − 4 1 <path d="M983 90 l0 -0 c4,-6.7,10,-10,18,-10 H400000v40 H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7 s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744 c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30 c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722 c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5 c53.7,-170.3,84.5,-266.8,92.5,-289.5z M1001 80h400000v40h-400000z">

− 1 16 -\frac{1}{16} − 16 1

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

Struggling with College Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Evaluate the radical.
$-\sqrt{\frac14}$

$\frac12$

$-\frac12$

$-\frac{1}{16}$

No real solution (Imaginary)

Verified step by step guidance

Identify the expression under the square root: $ \frac{1}{4} $.

Calculate the square root of $ \frac{1}{4} $. Recall that the square root of a fraction $ \frac{a}{b} $ is $ \frac{\sqrt{a}}{\sqrt{b}} $.

The square root of $ \frac{1}{4} $ is $ \frac{1}{2} $ because $ \sqrt{1} = 1 $ and $ \sqrt{4} = 2 $.

Substitute the square root value back into the original expression: $ -14 - \frac{1}{2} $.

Simplify the expression by combining the terms: $ -14 - \frac{1}{2} $. This involves converting $-14$ to a fraction with a common denominator if necessary.