Simplify each radical expression. Assume all variables
represent positive real numbers
�ãa^10
again when I post it does not read right.
it is sqrt a^10
One of the rule of exponents tells us that the square root of a number a raised to an exponent n is the same number raised to an exponent of n/2.
Thus the square-root of a² is a2/2 = a¹
In the particular example given,
sqrt(a10)
= a10/2
= a5
To simplify the radical expression a^10, we can apply the property of radicals that states the square root of a product is equal to the product of the square roots.
Starting with a^10, we can rewrite it as (a^5)^2, since raising a number to the power of 2 is the same as taking its square.
Applying the property, we simplify the expression as:
√(a^10) = √((a^5)^2) = a^5
To simplify the radical expression a^10, we need to identify the perfect square factors of a^10.
Since 10 is an even exponent, we can divide it by 2: 10 ÷ 2 = 5.
So, a^10 can be expressed as (a^5)^2.
The square root of a^10, therefore, simplifies to a^5.
Hence, the simplified radical expression for a^10 is a^5.