Final answer:
The square root of 648 in non-decimal form is simplified into prime factors and then expressed as 36√(2), using the fact that 2² equals 4 and 3² equals 9.
Step-by-step explanation:
The question asks for the square root of 648 not in decimal form. To do this, we simplify the square root by factoring 648 into its prime factors, which are 2, 2, 2, 3, 3, and 3.
The square root of 648 can be written as √(2³ × 3³) which can be further simplified to 2²×3²×√(2). Since 2² is 4 and 3² is 9, the simplified version becomes 4×9×√(2) or 36×√(2).
This represents the square root of 648 in a simplified radical form without the use of decimals.
To find the square root of 648 in not decimal form, we can use exponential notation. The number can be expressed as 8.32407 × 10-³. The number 8.32407 contains all of the significant figures, while 10-³ locates the decimal point. Therefore, the square root of 648 in not decimal form is approximately 8.32407 × 10-³.