Square root of 0.9 multiplied by square root of 1.6. Answer in decimal form. Anyone, please help.
The Correct Answer and Explanation is:
To find the value of:0.9×1.6\sqrt{0.9} \times \sqrt{1.6}0.9×1.6
Step 1: Use a property of square roots
We apply the rule:a×b=a×b\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}a×b=a×b
So:0.9×1.6=0.9×1.6\sqrt{0.9} \times \sqrt{1.6} = \sqrt{0.9 \times 1.6}0.9×1.6=0.9×1.6
Step 2: Multiply the numbers inside the square root
0.9×1.6=1.440.9 \times 1.6 = 1.440.9×1.6=1.44
Step 3: Take the square root of the product
1.44=1.2\sqrt{1.44} = 1.21.44=1.2
Final Answer:
0.9×1.6=1.2\sqrt{0.9} \times \sqrt{1.6} = 1.20.9×1.6=1.2
Explanation
To solve this expression, we begin by using the mathematical rule that allows us to combine two square roots into one. This is only valid when both values inside the square roots are non-negative, which is true in this case since 0.9 and 1.6 are both positive. This rule simplifies calculations by reducing two radicals into one.
When we multiply 0.9 by 1.6, we get 1.44. You can think of 0.9 as 9 divided by 10, and 1.6 as 16 divided by 10. So the product becomes (9 × 16) ÷ (10 × 10) = 144 ÷ 100 = 1.44. This step ensures accuracy before applying the square root.
Next, we take the square root of 1.44. This step requires either recognizing perfect squares or using a calculator. The square root of 1.44 is 1.2 because 1.2 multiplied by itself equals 1.44 (1.2 × 1.2 = 1.44).
Understanding how square roots and multiplication interact is useful in both pure mathematics and applied fields such as physics or engineering. It helps simplify complex expressions and can be useful when working with measurements, formulas, or data analysis.
So, putting it all together, 0.9×1.6=1.44=1.2\sqrt{0.9} \times \sqrt{1.6} = \sqrt{1.44} = 1.20.9×1.6=1.44=1.2. This clean and exact result shows how mathematical properties can make calculations more manageable and efficient.
