Question

Square root of 40 with steps

Answer 1

To find the square root of 40, we can use either long division method or prime factorization method.

Method 1: Long division method

Step 1: Write down the number 40 under the radical sign:

√40

Step 2: Find the pair of closest perfect squares, one of which is less than or equal to 40. The closest perfect square to 40 is 36, which is 6².

Step 3: Divide 40 by 36, and write the quotient above the number 40:

√40 = √36 × √(40/36)

Step 4: Simplify the expression under the radical sign:

√40 = 6 × √(4/9 × 10)

Step 5: Simplify further by taking out the perfect square factor from inside the radical:

√40 = 6 × √4 × √(10/9)

Step 6: Simplify the expression under the radical sign again:

√40 = 6 × 2 × √(10/9)

Step 7: Multiply the factors outside the radical sign:

√40 = 12 × √(10/9)

Therefore, the square root of 40 is equal to 12√(10/9).

Method 2: Prime factorization method

Step 1: Find the prime factorization of 40:

40 = 2² × 5

Step 2: Separate the perfect square factors from the remaining factors:

40 = 4 × 10

Step 3: Take the square root of the perfect square factor:

√4 = 2

Step 4: Write the remaining factors under the radical sign:

√10

Step 5: Combine the factors:

√40 = √4 × √10 = 2 × √10

Therefore, the square root of 40 is equal to 2√10.