Can you help with these please? I'm so bad at them!!
1. square root 160
2. square root -99
3. - Square root -169
4. square root -12
1. 4 times squareroot 10
2. 3 times squareroot 11
3. 13
4. 2 times squareroot 3
Thanks SO much!! :) Helped a lot, from the answers, I could understand how to derive them! Thanks again!
-Angellove:)
Of course, I'd be happy to help you out with these questions!
1. To find the square root of 160, you can use a calculator or apply the long division method. However, let's try simplifying it a bit. We can break down 160 into its prime factors: 160 = 2 * 2 * 2 * 2 * 5. Since every pair of equal prime factors inside the square root can be taken out, we have √(160) = √(2 * 2 * 2 * 2 * 5) = 2 * 2 √5 = 4√5.
2. When it comes to square roots of negative numbers, like √(-99), the answer is considered to be a complex number. The square root of a negative number isn't defined within the set of real numbers. In the complex number system, we can express the square root of -99 as sqrt(99)i, where "i" is the imaginary unit (i^2 = -1). Therefore, the square root of -99 is sqrt(99)i.
3. Similar to the previous question, the square root of a negative number isn't defined within the set of real numbers. So, for √(-169), we need to consider complex numbers. Since 169 is equal to 13 * 13, we can write it as √(-169) = √(13 * 13) = 13i. Therefore, the square root of -169 is 13i.
4. For √(-12), again, we have a negative number under the square root, which requires complex numbers to represent the solution. We can break it down further as √(-1 * 12) = √(-1) * √(12) = i * 2√3 = 2i√3. Hence, the square root of -12 is 2i√3.
Remember that square roots of negative numbers involve complex numbers and require the use of the imaginary unit "i" to represent the solution.