I am assuming your question should be formatted as follows: 9(sqrt(2)) + 5(sqrt(3)) We want to try make the roots have the same number in them, we would usually do this by moving numbers outside the sqrt to the inside and finding factors of them both that are square numbers, but I can see that that will not work for this question with numbers that I can do in my head. If you know all your square numbers and their multiples by heart then you might be able to solve this. But for us mortals it is time to pull out the calculator. 21.388176
5 root 2
Square root of 6
-3
I will use "root" as a symbol for square root. I assume you want to get rid of the square root in the denominator; this will usually bring some square root into the numerator.If you have the square root by itself, or as a factor, multiply numerator and denominator by this square root. Example:3 / root(2) = 3 x root(2) / root(2) x root(2) = 3 x root(2) / 2.If the square root is added or subtracted with something else, multiply with a "complement", as in the following example:1 / root(2) + 5The "complement" is the same expression, but changing the plus sign to a minus sign. Multiply numerator and denominator aby root(2) - 5:root(2) - 5 / (root(2) + 5)(root(2) - 5)= (root(2) - 5) / (2 - 25)= (root(2) - 5) / -23= -(root(2) - 5) / 23
21. The nearest square number is 12321 - which is 1112.
5 root 2
15
You can always add radicals, but you can't simplify unless the radicands have a common factor. For example, the square root of 20 plus the square root of 45 equals 2 times the square root of 5 plus 3 times the square root of 5, which is 5 times the square root of 5.
-2 and -3Check:(-2) + (-3) = -5(-2)(-3) = 6Thus -2 and -3 are not the required numbers. let's find them: x + y = -6xy = -5 y = -x -6x(-x - 6) = -5-x^2 - 6x = -5x^2 + 6x = 5x^2 + 6x + 9 = 5 + 9(x + 3)^2 = 14x + 3 = (+ & -)square root of 14x = -3 (+ & -)square root of 14x = -3 + square root of 14 or x = - 3 - square root of 14y = -x - 6y = 3 - square root of 14 - 6 or y = 3 + square root of 14 - 6y = -3 - square root of 14 or y = -3 + square root of 14Check:(-3 + square root of 14) + (-3 - square root of 14) = -6(-3 + square root of 14)(-3 - square root of 14) = -5 ?(-3)^2 - (square root of 14)^2 = -5 ?9 - 14 = -5Check also tow other numbers.
Square root of 6
-3
95
I will use "root" as a symbol for square root. I assume you want to get rid of the square root in the denominator; this will usually bring some square root into the numerator.If you have the square root by itself, or as a factor, multiply numerator and denominator by this square root. Example:3 / root(2) = 3 x root(2) / root(2) x root(2) = 3 x root(2) / 2.If the square root is added or subtracted with something else, multiply with a "complement", as in the following example:1 / root(2) + 5The "complement" is the same expression, but changing the plus sign to a minus sign. Multiply numerator and denominator aby root(2) - 5:root(2) - 5 / (root(2) + 5)(root(2) - 5)= (root(2) - 5) / (2 - 25)= (root(2) - 5) / -23= -(root(2) - 5) / 23
21. The nearest square number is 12321 - which is 1112.
2 × 3 × √5 = 6√5 2 × 3 × √5 ≈ 13.4
sqrt(4) = 2 sqrt(9) = 3 Therefore, the square root of 4 plus the square root of 9 is equal to 2 + 3 = 5.
If you add 5 to -2, you can get 3