Simplifying the Expression: 1/2×1/2√2
In this article, we will explore the simplification of the mathematical expression: 1/2×1/2√2.
Introduction
The expression 1/2×1/2√2 may seem complex at first glance, but it can be simplified using basic algebraic rules and properties of radicals. In this article, we will break down the expression into its constituent parts and simplify it step by step.
Simplifying the Expression
To simplify the expression, we can start by multiplying the two fractions:
1/2 × 1/2 = 1/4
Now, we are left with:
1/4√2
Simplifying the Radical
To simplify the radical, we need to recall that √2 can be expressed as:
√2 = 2^1/2
So, we can rewrite the expression as:
1/4 × 2^1/2
Rationalizing the Denominator
To rationalize the denominator, we can multiply the expression by 2^1/2/2^1/2, which is equivalent to multiplying by 1:
1/4 × 2^1/2 × 2^1/2/2^1/2
This simplifies to:
1/2^1/2
Simplifying Further
We can further simplify the expression by recalling that 2^1/2 is equivalent to √2:
1/√2
Conclusion
In conclusion, the simplified expression for 1/2×1/2√2 is 1/√2. By applying basic algebraic rules and properties of radicals, we were able to simplify the expression and arrive at a more elegant and concise form.
