TenMarks teaches you how to find and evaluate roots.
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Learn to Evaluate Roots In this lesson, let's learn how we find roots. Roots are the following, if we take a number and multiply it by itself, we get the product, 7x7 is 49. So a number which when multiplied by itself gives a product. Seven is called a square root of 49. So if a number is multiplied by itself to get the product, the number is the square root of the product. So that’s the thing that we need to remember when we’re trying to find roots. So let's try and do a few problems. We need to find in Part A the square root of 49. Now this is the symbol for square root or root. If there is no number around it; that means it's the square root. So if we are trying to find the square root for 49, we need to find a number which when multiplied by itself will give us 49. Well, what’s that number, 7x7 gives me 49. So the square root of 49 is seven. All we need to do is find the number which when multiplied by itself will give you the product. The second thing we need to remember is a square root of 49 equals seven, then 7x7=49. So, square root of 49 equals seven, 7x7=49. They are reversible operations. So, let's do Part B. Part B is we need to find the cube root of -125. The number three before the root sign signifies that instead of the number being multiplied twice, it needs to be multiplied thrice. So which number when multiplied by itself three times will give us -125? Do we know what it is? It's actually -5, -5x-5 is +25, x -5 is -125. So -5 multiplied by itself three times gives us -125. So the cube root of -125=-5. That’s the answer we’re looking for. Let's do the third one right here, which is we need the square root of 1/4, which means what fraction when multiplied by itself gives us 1/4? Well, I just gave it to you. 1/2x1/2 gives us 1/4. Why? 1x1 is 1, 2x2 is 4. So 1/2 x 1/2 is 1/4 which means square root of 1/4=1/2. It's the same exact principle. What number multiplied by itself will give us the value within the root? Well, the number is 1/2. Let's try a slightly difficult problem which says evaluate the expression when A=9 and B=7. We need to take the square root of A+B. Well what is A+B? Let's substitute it. Instead of A, let's put it nine. Instead of B, let's put it seven. What do I get? The square root of 9+7 is 16. In order the square root of 16, we need to find two numbers or a number when multiplied by itself equals 16. Well, that’s four, right? 4x4 gives me 16. So the square root of 16 is 4. We simply find the number that when multiplied by itself gives you the number in underneath the root side.