Posts Tagged ‘EXPRESSION’

Problem 695

Evaluate the expression: log100




log 100

log 10^{2}= 2 log 10

we know log 10 = 1

log 100 = 2(1) = 2


Exponential Expression


Exponential Expression

If a is a real number and n is a natural number,

 an  =  a .a .a ……a,

n factors of a

where n is the exponent, a is the base, and an is an exponential expression.

Exponents are also called powers.


For example, the product  2 . 2 . 2 . 2 . 2  is written

2 . 2 . 2 . 2 . 2 = 25.

5 factors of 2

The number 5 shows that 2 is used as a factor 5 times. The number 5 is the

exponent, and 2 is the base.

25   Exponent


Finding root a^2

Finding \sqrt{ a^{2}}

In the expression \sqrt{ a^{2}}, the radicand is a perfect square. It is tempting to think

that \sqrt{ a^{2}}= a, but we see below that this is not the case.

Suppose a = 5. Then we have \sqrt{ 5^{2}}, which is\sqrt{25}  , or 5.

Suppose a = -5. Then we have \sqrt{ -5^{2}},which is\sqrt{25}  , or 5.

Suppose a = 0  . Then we have \sqrt{ 0^{2}}which is\sqrt{0}  , or 0.

The symbol \sqrt{ a^{2}}never represents a negative number. It represents the

principal square root of  a2. Note the following.


SIMPLIFYING \sqrt{ a^{2}}

a ≥ 0 \rightarrow    \sqrt{ a^{2}}= a

if a is positive or 0 ,the principal square root of \sqrt(a) is a.

a < 0 \rightarrow  \sqrt{ a^{2}}= -a

If a is negative, the principal square root of \sqrt(a) is the opposite of a.

In all cases, the radical expression represents the absolute value of a.



For any real number a, \sqrt{ a^{2}}=  \left | a \right | . The principal (nonnegative) square

root of a2 is the absolute value of a.





The symbol √ is called a radical.

An expression written with a radical is called a radical expression.

The expression written under the radical is called the radicand.

These are radical expressions:

√5 ,  √a , -√5x