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.
Square root of 40 with steps
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