Evaluate the following
√3√12√40√48
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
√3√12√40√48 = √3*12*40*48
√3√12√40√48 = √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
Simplify it into the product of an integer and a radical.
We do this by listing each product combo of 69120
Check for integer square root values below:
√69120 = √1√69120
√69120 = √2√34560
√69120 = √3√23040
√69120 = √4√17280
√69120 = √5√13824
√69120 = √6√11520
√69120 = √8√8640
√69120 = √9√7680
√69120 = √10√6912
√69120 = √12√5760
√69120 = √15√4608
√69120 = √16√4320
√69120 = √18√3840
√69120 = √20√3456
√69120 = √24√2880
√69120 = √27√2560
√69120 = √30√2304
√69120 = √32√2160
√69120 = √36√1920
√69120 = √40√1728
√69120 = √45√1536
√69120 = √48√1440
√69120 = √54√1280
√69120 = √60√1152
√69120 = √64√1080
√69120 = √72√960
√69120 = √80√864
√69120 = √90√768
√69120 = √96√720
√69120 = √108√640
√69120 = √120√576
√69120 = √128√540
√69120 = √135√512
√69120 = √144√480
√69120 = √160√432
√69120 = √180√384
√69120 = √192√360
√69120 = √216√320
√69120 = √240√288
√69120 = √256√270
From that list, the highest factor with an integer square root is 2304
Therefore, we use the product combo √69120 = √2304√30
Evaluating square roots, we see that √2304 = 48
Simplifying our product of radicals, we get our answer:
Group square root terms for 48
48√30
Final Answer:
Common Core State Standards In This Lesson
How does the Square Roots and Exponents Calculator work?
* 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: √a√b√c√d√e
* 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?
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
