What is the simplified form of 5√18?

The simplified form of 5√18 is 15√2.

To simplify 5√18, we first need to simplify the square root of 18. The number 18 can be factorised into its prime factors: 18 = 2 × 3 × 3. This can be written as 18 = 2 × 3². The square root of 18 is therefore √(2 × 3²). Using the property of square roots, √(a × b) = √a × √b, we can split this into √2 × √(3²). Since the square root of a square number is just the number itself, √(3²) simplifies to 3. So, √18 simplifies to 3√2.

Now, we multiply this simplified form by 5. So, 5√18 becomes 5 × 3√2. Multiplying the numbers outside the square root gives us 15√2. Therefore, the simplified form of 5√18 is 15√2.

This process involves understanding how to factorise numbers and apply properties of square roots, which are key skills in GCSE Maths. By breaking down the problem step-by-step, you can simplify more complex expressions involving square roots with confidence.