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2. Simplification of Radical Expressions - Algebra - Socratic

   socratic.org/algebra/radicals-and-geometry-connections/simplification-of...

   There are two common ways to simplify radical expressions, depending on the denominator. Using the identities \sqrt {a}^2=a and (a-b) (a+b)=a^2-b^2, in fact, you can get rid of the roots at the denominator. Case 1: the denominator consists of a single root. For example, let's say that our fraction is {3x}/ {\sqrt {x+3}}.

3. Multiplication and Division of Radicals - Algebra - Socratic

   socratic.org/algebra/radicals-and-geometry-connections/multiplication-and...

   When you have a root (square root for example) in the denominator of a fraction you can "remove" it multiplying and dividing the fraction for the same quantity. The idea is to avoid an irrational number in the denominator. Consider: #3/sqrt2#. you can remove the square root multiplying and dividing by #sqrt2#; #3/sqrt2*sqrt2/sqrt2#.

4. How do you add #sqrt(10) + sqrt(10)#? - Socratic

   socratic.org/questions/how-do-you-add-sqrt-10-sqrt-10

   Think at the two squares as 2 similar objects that, as x, can be added giving x+x=2x so: sqrt(10)+sqrt(10)=2sqrt(10)= now 2 can "enter" into the root: =sqrt(4*10)=sqrt(40)

5. How do you find the square root of 10? + Example - Socratic

   socratic.org/questions/how-do-you-find-the-square-root-of-10

   sqrt(10) ~~ 3.16227766016837933199 is not simplifiable. 10 = 2xx5 has no square factors, so sqrt(10) is not simplifiable.

6. How do you simplify #sqrt(10)#? - Socratic

   socratic.org/questions/how-do-you-simplify-sqrt-10

   Since no factor is repeated, the square root cannot be simplified. It is an irrational number a little larger than 3 = √9. sqrt (10) is already in simplest form. The prime factorisation of 10 is: 10 = 2 * 5 Since no factor is repeated, the square root cannot be simplified. It is an irrational number a little larger than 3 = sqrt (9).

7. What is the square root of negative one? + Example - Socratic

   socratic.org/questions/what-is-the-square-root-of-negative-one

   The principal square root of minus one is i. It has another square root -i. I really dislike the expression "the square root of minus one". Like all non-zero numbers, -1 has two square roots, which we call i and -i. If x is a Real number then x^2 >= 0, so we need to look beyond the Real numbers to find a square root of -1. Complex numbers can be thought of as an extension of Real numbers from ...

8. What is the square root of 5 times the square root of 10?

   socratic.org/questions/what-is-the-square-root-of-5-times-the-square-root-of-10

   1 Answer. Alan P. Sep 10, 2015. √5 ⋅ √10 = 5√2. (assuming only primary roots; otherwise −5√2 is a secondary answer) Explanation: √5 ⋅ √10. XXX = √5 ⋅ √5 ⋅ √2.

9. How do you find the square root of #100# - Socratic

   socratic.org/questions/55a51e47581e2a3bd418ca3f

   The (positive) square root of 100 is 10. -10 is also a square root of 100. We write the positive square root of 100 as sqrt(100) A square root of a number n is a number x such that x^2 = n. As for how do you find the square root of 100, you should encounter 100 = 10^2 often enough that it will become obvious. 10^0 = 1 10^1 = 10 10^2 = 10 xx 10 = 100 10^3 = 10 xx 10 xx 10 = 1000 etc. So if you ...

10. How do you evaluate #log_10 sqrt(10)#? - Socratic

    socratic.org/questions/how-do-you-evaluate-log-10-sqrt-10

    Explanation: logabc. a is the base, b is the number and c is the power/exponent. log10√10. = log10101 2. The properties of a logarithmic function allows the exponent to be "brought" down as such: = log10101 2. = (1 2)log1010. When the base is equal to the logarithmic number , the result is 1 eg. (log22 = 1,log33 = 1,log1000 1000 = 1).

11. Can square root of 10 be simplified? - Socratic

    socratic.org/questions/can-square-root-of-10-be-simplified

    Explanation: Since 10 = 2 ⋅ 5, we can rewrite this as. √2 ⋅ 5, which is also equal to. √2 ⋅ √5. However, since we have no perfect square factors, this is about as simplified as we can get. As a decimal, this is approximately. 3.1622.