What is the simplified form of square root of 45
The Correct Answer and Explanation is:
Simplified Form of √45:
45=35\sqrt{45} = 3\sqrt{5}45=35
Explanation
To simplify the square root of 45, we need to break it down into its prime factors and look for perfect squares.
Step 1: Prime Factorization of 45
We start by factoring 45:45=9×545 = 9 \times 545=9×5
Here, 9 is a perfect square because:9=3×3=329 = 3 \times 3 = 3^29=3×3=32
So, we can rewrite the square root as:45=9×5\sqrt{45} = \sqrt{9 \times 5}45=9×5
Step 2: Use the Property of Square Roots
One of the main properties of square roots is:a×b=a×b\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}a×b=a×b
Applying this:45=9×5\sqrt{45} = \sqrt{9} \times \sqrt{5}45=9×5
Since 9=3\sqrt{9} = 39=3, we get:45=35\sqrt{45} = 3\sqrt{5}45=35
This is the simplified form of the square root of 45. It cannot be simplified further because 5 is a prime number and not a perfect square.
Why Simplification Matters
Simplifying square roots helps in:
- Solving algebraic equations
- Reducing complexity in math expressions
- Understanding irrational numbers more clearly
In this case, 45≈6.708\sqrt{45} \approx 6.70845≈6.708, but 353\sqrt{5}35 is a more exact form, especially useful in algebra and geometry where precision is key.
Final Answer:
45=35\boxed{\sqrt{45} = 3\sqrt{5}}45=35
