square root

To do this, we need rationalize the denominator. This means get rid of the radical: Multiply top and bottom by sqrt(5) 2sqrt(5)/sqrt(5) * sqrt(5) sqrt(5) * sqrt(5) = sqrt(25) so we have: 2sqrt(5)/sqrt(25) sqrt(25) = 5, so we have: 2sqrt(5)/5

7sqrt(3) is broken down. sqrt(12) is not broken down. Let's find all the factors of 12 and see if we stumble on a perfect square: 1 * 12 2 * 6 3 * 4 4 is a perfect square, since sqrt(4) = 2. So sqrt(12) = sqrt(3 * 4) We pull the sqrt(4) = 2 outside the radical and rewrite our problem as...

(Sqrt(24) + sqrt(96))/2 Simplify sqrt(24) 24 = 6 * 4 where 4 is the perfect square sqrt(24) = 2 * sqrt(6) Simplify sqrt(96) 96 = 16 * 6 where 16 is the perfect square sqrt(96) = 4 * sqrt(6) Simplified, we have: (2 * sqrt(6) + 4 * sqrt(6))/2 6 * sqrt(6)/2 3 * sqrt(6)

1/n^2 = 3/192 Cross multiply: 192 * 1 = 3 * n^2 3n^2 = 192 Divide each side by 3: 3n^2/3 = 192/3 Cancel the 3's on the left side: n^2 = 64 Take the square root of both sides: n = 8 or -8

n^2 - 1 = -99/100 Add 1 (100/100) to each side: n^2 - 1 + 1 = -99/100 + 100/100 Cancel the 1's on the left side: n^2 = 1/100 Take the square root of both sides: n = 1/10 or -1/10

n^2 = 6&1/4 6&1/4 = 25/4 n^2 = 25/4 Take the square root of each side: n = 5/2 or -5/2

n^2 = 1/4 Take the square root of each side: n = 1/2

n^2 + 9 = 34 Subtract 9 from each side: n^2 + 9 - 9 = 34 - 9 n^2 = 25 Take the square root of each side: n = 5

n^2 = 64 Take the square root of each side: sqrt(n^2) = sqt(64) n = 8

Kamille is calculating the length of diagonal on a picture board and gets a solution of the square root of 58. She needs to buy the ribbon to put across the diagonal of the board, so she estimates that she will need at least 60 inches of ribbon to cover the diagonal. Is she correct? Explain...

find the two square roots of 81 When we multiply 9 * 9, we get 81 When we multiply -9 * -9, we get 81 So our two square roots of 81 are: -9, 9

square root of the sum of 2 variables The phrase 2 variables means we choose 2 arbitrary variables, let's call them x and y: x, y The sum of 2 variables means we add: x + y Square root of the sum of 2 variables is written as: sqrt(x + y)

Six is the principal square root of 36 The two square roots of 36 are: +6 -6 The positive square root is known as the principal square root, therefore, this is true.

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen? Let n be our original number. Square the number...

The square of a number is positive N ca be positive or negative, so test both scenarios: Take a positive number n. n^2 = n^2 * n^2 or Positive * Positive which is positive Take a negative number n (-n)^2 = -n * -n or Negative * Negative which is positive (-n)^2 = n^2

what two values can d have if d squared is 9 d^2 = 9 Using our calculator, we get: d = (-3, 3}

If m% of m is 36, then m is? m% = m/100, so we have: m/100 * m = 36 m^2/100 = 36 Cross multiply and we get: m^2 = 3600 We use our radical expressions simplifier to get: m = 60

Each side of a square is lengthened by 3 inches . The area of this new, larger square is 25 square inches. Find the length of a side of the original square. area of a square is s^2 New square has sides s + 3, so the area of 25 is: (s + 3)^2 = 25 Solving for s, we get: s = 2

Explain the relationship between "squaring" a number and finding the "square root" of a number. Use an example to further explain your answer. Squaring a number means raising it to the power of 2 The square root of a number undoes a square of a number. So square root of x^2 is x x squared is...

Square root of 9136 divided by 43 First, take the square root of 9136 in our calculator: 4 * sqrt(571) Now divide this by 43: 4 * sqrt(571) / 43