To simplify radicals for kids, teach them to find perfect square factors or use a factor tree, looking for pairs of identical prime numbers; each pair lets one number come out of the radical, while leftovers stay inside, multiplying with any numbers already outside. For example, 48 4 8 √ becomes 16 ⋅ 3 1 6 ⋅ 3 √ , so 4 3 4 3 √ , because 16 is a perfect square and 4 comes out.
Solve Radical Equations
Find the unit digits we get after squaring the numbers from 1 to 10 in the below table. Hence, from the above table we can figure out if any perfect square ends with the above digits at the unit place, then its square root will have the same respective number at the unit place. For example, the square root of 81 is 9.
In order to simplify a radical:
Square Root of 75 by Prime Factorization Method
The prime factorisation of 75 is 3×5×5. Thus, √75 = √3. √5. √5 = 5√3.
The number 75 is not a perfect square because it cannot be expressed as the product of an integer multiplied by itself. Its prime factors (3 and 5²) do not form perfect pairs for all primes, leaving an irrational square root.
Square root of 45 is 6.7082039325 it is a number which when multiplied by itself results in 45. Root of 45 is written as √45 or (45)1/2. Simplified radical form of the square root of 45 is √(45) = 3√5.
What is the square root of 48 in simplified form? The square root of 48 in simplified form is 4√3.
The square root of 49 can be found using the prime factorization method. To find the value, we should know the prime factorization of 49. Thus, the prime factorization of a number 49 is 7×7. Hence, the square root of 49 is equal to 7.
Answer and Explanation:
To simplify 5 √48 we can do so by factoring √48 into √16 x √3: 5 √48. 5(√16)(√3) 5(4)(√3)
The square root of 48 is considered to be an irrational number since it cannot be expressed in the form of p/q and the decimal part of the value of the square root of 48 is never-ending. There are two different ways to find the square root of 48, such as prime factorization and the long division method.