5 times the square root of 176 minus 3 times the square root of 99 plus 4 times the square root of 162

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`5sqrt176-3sqrt99+4sqrt162` (given)

Expressing radicals in the form of exponents

`=5(176)^(1/2)-3(99)^(1/2)+4(162)^(1/2)`

`=5(4^2*11)^(1/2)-3(3^2*11)^(1/2)+4(9^2*2)^(1/2)`

Using the exponent property of `(a*b)^n=a^n*b^n`

`=5*4*(11)^(1/2)-3*3*(11)^(1/2)+4*9*(2)^(1/2)`

`=20*(11)^(1/2)-9*(11)^(1/2)+36*(2)^(1/2)`

Again, expressing in the form of radicals

`=20sqrt11-9sqrt11+36sqrt2`

subtracting the like radicals

`=11sqrt11+36sqrt2`

**This is the required answer.**

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