Simplify Square Root of Square Root Expression

Nested Square Root Expressions

Simplify the nested radicals shown in the image.

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Simplifying an expression means to make that expression as simple as possible by reducing the complexity of the expression.

Simplifying an expression will produce a simpler form of that expression. The simplified version of an expression should have fewer terms, factors, and roots. Simplification should reduce the overall length of the expression.

Simplification is usually accomplished by grouping and combining like terms, or factoring and/or cancelling common multipliers, etc.

However, simplification stops short of evaluation in most cases.

For example, the square root of 20 can be simplified as follows:

√(20) = √(4 * 5) = √(2² * 5) = 2√(5)

The square root of 20 can be simplified to 2√(5).

Simplification is not the same as evaluating the expression.

Evaluating an expression means to arrive at a single number.

For example, evaluating the square root of 20 means:

√(20) = ±4.4721359549996

The square root of 20 can be evaluated as ±4.4721359549996.