Square root of 59? Please leave an explanation/steps because when I search this question, all the answers have no explanation..

7.681

Step-by-step explanation:

Step 1: Starting from the right, we will pair up the digits 59 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.

Step 2: Think of a number whose square is less than or equal to 59. In this case, that number would be 7.

Step 3: Dividing by 59 by 7 with quotient set as 7, we get a remainder of 10.  

Step 4: Drag a pair of 0’s down and fill it next to the remainder to make it 1000.  

Step 5: The divisor, in this case 7 is doubled and written below. Now, we have 14X as the new divisor, and we need to find a value of X that makes the product of 14X × X less than or equal to 1000. In this case, 146 is the required value

Step 6: The number 6 is placed in the quotient after a decimal place. The new divisor for the next division will be 146 + 6 = 152.

Proceeding in the same manner and repeating from step 4, we can calculate the rest of the decimals.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)