 # sqrt3sqrt12sqrt40sqrt48

## Enter square root or exponent statement:

Evaluate √3124048

## Term 1 has a square root, so we evaluate and simplify:

We have a product of 4 square root terms
The product of square roots is equal to the square root of the products
3124048 = √3*12*40*48
3124048 = √69120
Simplify √69120.

Checking square roots, we see that 2622 = 68644 and 2632 = 69169.
Our answer in decimal format is between 262 and 263
Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 69120 checking for integer square root values below:
69120 = √169120
69120 = √234560
69120 = √323040
69120 = √417280
69120 = √513824
69120 = √611520
69120 = √88640
69120 = √97680
69120 = √106912
69120 = √125760
69120 = √154608
69120 = √164320
69120 = √183840
69120 = √203456
69120 = √242880
69120 = √272560
69120 = √302304
69120 = √322160
69120 = √361920
69120 = √401728
69120 = √451536
69120 = √481440
69120 = √541280
69120 = √601152
69120 = √641080
69120 = √72960
69120 = √80864
69120 = √90768
69120 = √96720
69120 = √108640
69120 = √120576
69120 = √128540
69120 = √135512
69120 = √144480
69120 = √160432
69120 = √180384
69120 = √192360
69120 = √216320
69120 = √240288
69120 = √256270

From that list, the highest factor that has an integer square root is 2304.
Therefore, we use the product combo √69120 = √230430
Evaluating square roots, we see that √2304 = 48

69120 = 48√30

## Group square root terms for 48

48√30

48√30

### How does the Square Roots and Exponents Calculator work?

Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:
* The square root of n denoted as √n
* The square root of the fraction n/m denoted as √n/m
* n raised to the xth power denoted as nx (Write without exponents)
* n raised to the xth power raised to the yth power denoted as (nx)y (Write without exponents)
* Product of up to 5 square roots: √abcde
* Write a numeric expression such as 8x8x8x8x8 in exponential form
This calculator has 1 input.

### What 3 formulas are used for the Square Roots and Exponents Calculator?

1. √n2 = ±n

For more math formulas, check out our Formula Dossier

### What 5 concepts are covered in the Square Roots and Exponents Calculator?

exponent
The power to raise a number
fraction
how many parts of a certain size exist
a/b where a is the numerator and b is the denominator
power
how many times to use the number in a multiplication
square root
a factor of a number that, when multiplied by itself, gives the original number
√x
square roots and exponents